Answer: 1 knife costes £5.52
Step-by-step explanation:
Let a knife costes £x and a spoon costes £y
Hence, we obtain a system of equations:
x=3y (1)
12x+9y=82.80 (2)
Divide both parts of the equation (2) by 3:
x=3y
4x+3y=27.6 (3)
We substitute the value of x=3u into equation (3):
4(3y)+3y=27.6
12y+3y=27.6
15y=27.6
Divide both parts of the equation by 15:
y=£1.84
x=3y
x=3(1.84)
x=£5.52
5. Sima invests some money in an account that earns a fixed rate of interest
compounded annually. The amounts of the investment at the end of the first
three years are shown below
a) Determine the annual rate of compound interest earned.
b) How much did Sima invest?
Year. Total amount
1. $4240.00
2. $4494.40
3 $4764.06
Answer:
Step-by-step explanation: To solve this problem, we can use the following formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A is the total amount at the end of the period
P is the principal (initial investment)
r is the annual interest rate
n is the number of times the interest is compounded per year
t is the number of years
We can rearrange this formula to solve for r:
r = n * ((A/P)^(1/n*t) - 1)
We can plug in the values for A, P, and t for each year to solve for the annual interest rate:
Year 1:
r = n * ((4240.00/P)^(1/n*1) - 1)
r = 1 * ((4240.00/P)^(1/1) - 1)
r = (4240.00/P) - 1
r = 4240.00/P - 1
r = 4240.00 - P/P
r = 4240.00 - 1
r = 0.08
Year 2:
r = n * ((4494.40/P)^(1/n*2) - 1)
r = 1 * ((4494.40/P)^(1/2) - 1)
r = (4494.40/P)^(1/2) - 1
r = 4494.40/P - 1
r = 4494.40 - P/P
r = 4494.40 - 1
r = 0.08
Year 3:
r = n * ((4764.06/P)^(1/n*3) - 1)
r = 1 * ((4764.06/P)^(1/3) - 1)
r = (4764.06/P)^(1/3) - 1
r = 4764.06/P - 1
r = 4764.06 - P/P
r = 4764.06 - 1
r = 0.08
Since the annual interest rate is consistent at 0.08 for all three years, we can conclude that this is the annual rate of compound interest earned.
To solve for the principal, we can use the formula for compound interest again, this time solving for P:
P = A / (1 + r/n)^(n*t)
Plugging in the values for A, r, and t for each year, we get:
Year 1:
P = 4240.00 / (1 + 0.08/1)^(1*1)
P = 4240.00 / 1.08
P = 3925.93
Year 2:
P = 4494.40 / (1 + 0.08/1)^(1*2)
P = 4494.40 / 1.16
P = 3925.93
Year 3:
P = 4764.06 / (1 + 0.08/1)^(1*3)
P = 4764.06 / 1.24
P = 3925.93
Since the principal is consistent at $3925.93 for all three years, we can conclude that this is the amount Sima invested.
On a coordinate plane, an absolute value graph has a vertex at (negative 2, 1).
The graph of g(x) = |x – h| + k is shown on the coordinate grid. What must be true about the signs of h and k?
Both h and k must be positive.
Both h and k must be negative.
h must be positive and k must be negative.
h must be negative and k must be positive.
For the absolute value function g(x) = |x + 2| + 1, h must be negative and k must be positive.
What is an absolute value function?We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.
In piecewise terms | x | = x for x ≥ 0 and | x | = - x for x < 0.
We know the coordination of the vertex of an absolute value function
g(x) = |x - h| + k is, (h, k).
Given, An absolute value function has vertex coordinate (- 2, 1).
Therfore the absolue value function g(x) = |x - (-2)| + 1.
g(x) = |x + 2| + 1, The graph is shifted horizontally left by 2 units and up vertically by 1 unit so h must be negative and k must be positive.
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PLEASE HELP!!!!! I DONT UNDERSTAND THIS
The simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2, so option A is correct.
What is equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Given equation:
8y = -2x + 4
Divide both sides by 8,
8y / 8 = -2x / 8 + 4 / 8
Simplify the above expression,
y = -1 / 4x + 1 / 2
Therefore, the simplified version of 8y = -2x + 4 is y = -1 / 4x + 1 / 2.
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Quetion
a. Write the formula for the area A of a trapezoid. Ue b1 and b2 for the length of the bae, and ue h for the height. A=
b. Solve the formula for h. H=
c. Ue the new formula to find the height h of the trapezoid. The height of the trapezoid i
centimeter
The formula for the area A of a trapezoid [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex], the formula for the height of the trapezoid is [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] , and the height of the given trapezoid is 6cm.
(a) let us find the formula for the area A of a trapezoid as follows-
As b₁, b₂ being the lengths of the bases and 'h' is the height.
So, the formula for the area A of a trapezoid is given by-
[tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]
(b) Let us solve for the formula for the height h of the trapezoid as follows-
As the formula for the area A of a trapezoid is [tex]A= \frac{1}{2} (b_{1} + b_{2})h[/tex]
So, the formula for height h of the trapezoid can be given by -
[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]
(c) Let us find the new formula to find the height h of the trapezoid as follows-
Using, [tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex] to find the height h of the trapezoid.
So,
[tex]h= \frac{2A} {(b_{1} + b_{2})}[/tex]
[tex]h= \frac{2(72)} {16 +8}[/tex] --------(substituting the values of b₁ = 16, b₂ = 8, A = 72cm²)
h = 144/24
h = 6 cm
Hence, the height of the trapezoid is 6cm.
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The complete question is -
a. Write the formula for the area A of a trapezoid. Use b1 and b2 for the length of the base, and use h for the height. A=
b. Solve the formula for h. H=
c. Use the new formula to find the height h of the trapezoid. The height of the trapezoid in centimeters.
find the length of the curve. r(t) = 4t i + 8t3/2 j + 9t2 k, 0 ≤ t ≤ 1
The length of the curve [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex] is 13.
The given curve is defined by the parametric equation [tex]r(t) = 4t i + 8t^{3/2} j + 9t^{2}k, 0\leq t\leq 1[/tex].
The length of a curve is given by the formula
⇒ [tex]|| r(t) || = \int\limits^a_b {\sqrt{{(x')^{2}} + (y')^{2} + (z')^{2} } } \, dt[/tex]
where the variables x', y', z' are defined as
[tex]x' = \frac{d(4t)}{dt} = 4 \\y' = \frac{d(8t^{3/2})}{dt} = 12t^{1/2} \\x' = \frac{d(9t^{2})}{dt} = 18t\\[/tex]
Hence, substituting the values in the formula for the length
⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{(4)^{2}} + (12t^{1/2})^{2} + (18t)^{2} } } \, dt[/tex]
⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]
The given definite integral is in the form of
[tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \int\limits^a_b {\sqrt{{ax^{2} + bx + c}} } \, dx[/tex]
where P(x) is a polynomial of degree 2.
Writing the polynomial P(x) as
⇒ [tex]\sqrt{P(x)} = \sqrt{a}\sqrt{{(x + b_1)^{2} + c_1}} dx[/tex]
⇒ [tex]\int\limits^a_b {\sqrt{P(x)}} \, dx = \sqrt{a}\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx[/tex]
where [tex]b_1, c_1[/tex] are defined as
⇒ [tex]b_1= \frac{a}{2b} \\c1 = \frac{c}{a} - b_1^{2}[/tex]
Therefore, the solution will be
⇒ [tex]\int\limits^a_b {\sqrt{{(x + b_1)^{2} + c_1}}} \, dx = \frac{(b_1 + x)\sqrt{P(x)} + c_1log{(b_1 + x + \sqrt{P(x)}}}{2}[/tex]
Hence, solving the integral
⇒ [tex]|| r(t) || = \int\limits^0_1 {\sqrt{{16 + 144t + 324t^{2}} } \, dt[/tex]
we get the value as 13.
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1. A phone is reduced by 30% to a price of £120. Calculate the original cost of the system.
2. What is of £240?
3. Write 48 as a product of its prime factors in index form.
4. Factorise x² -2x-35.
5. Write 210,000,000 in standard form.
6. Solve: 2x + 7 ≤ -1.
7. Use prime factors to find the lowest common multiple of 270 and 84.
8. List the first 5 terms of the sequence 8n + 2.
9. Find the total perimeter of the sector shown, correct to one decimal place.
6cm
124°
10. Calculate (4.85x1025)+(1.7×10¹9), giving your answer in standard form correct to two
significant figures.
Answer:
1. Step by step explanation:- Since 120$ is obtained by reducing the price by 30% that is subtracting ORIGINAL COST from its 30%.
In order to obtain the Cost Price we shall add back the 30% to 120$ to obtain the Cost Price -
120+30%*120 = 120+36= 156 $ . (Ignore the currency. Answer remains unaffected )
2. Question is incomplete.
3. 48=2*2*2*2*3
4. Factorization of x^2-2x-35 is
=x^2-7x+5x-35 (-7x+5x= -2x)
=x(x-7)-5(x-7) (Taking x common from the first () and 5 from the second bracket)
=(x-5)(x-7)
Factors are 7 and 5.
5. 2.1*10^8
6. For this question it is to be assumed that -
2x+7=-1
Now normally solving the equation we get
2x=-1-7
=> 2x= -8
=> x= -4
7. Multiples of 270 = 3*3*3*2*5
Multiples of 84 = 2*2*3*7
Common multiples = 2*3=6
8. First 5 terms can be obtained by putting (1,2,3,4,5) serially in the equation 8n+2
8*1+2=10, 8*2+2= 18, 8*3+2=26 , 8*4+2=34, 8*5+2= 42
you are dealt five cards from a thoroughly shfuffeld standard deck of cards. what is the probability that you get a full hosue.
The probability of drawing 3 aces and 2 kings is 9.23×[tex]10^{-6}[/tex] and the probability of a “full house” is 0.00144.
5 cards are drawn from a standard deck of 52 cards.
a) Probability that we draw 3 aces and 2 kings
Number of cards = 52
No of aces = 4
No of kings = 4
Number of cards drawn = 5
So, the probability becomes,
Text, letter
Description automatically generated with medium confidence
[tex]4C_{3}4C_{2}[/tex]/[tex]52C_{5}[/tex]
On simplification,
= 24 / 2598960
= 9.23×[tex]10^{-6}[/tex]
So the probability of drawing 3 aces and 2 kings is 9.23 × [tex]10^{-6}[/tex]
b) a “full house” (3 cards of one kind and 2 cards of another kind)
Since there are 13 sets of each type, we have to select any 2 kinds of it.
The probability becomes
(2×[tex]13 C_{2}[/tex]×[tex]4C_{3}[/tex][tex]4C_{2}[/tex])/[tex]52C_{5}[/tex]
On simplification,
= 3744 / 2598960
= 0.00144
So, The probability of a “full house” is 0.00144.
Therefore, the probability of drawing 3 aces and 2 kings is
9.23×[tex]10^{-6}[/tex] and the probability of a “full house” is 0.00144.
The possibility is the department of arithmetic concerning numerical descriptions of ways in all likelihood an event is to arise, or how in all likelihood it's miles that a proposition is authentic. The opportunity of an occasion varies between zero and 1, wherein, more, or less speaks to me, 0 suggests the impossibility of the event and 1 shows reality. The better the probability of an event, the much more likely it's far that the event will arise.
An easy example is the tossing of a fair (unbiased) coin. for the reason that coin is fair, the 2 effects ("heads" and "tails") are each equally probable; the opportunity of "heads" equals the possibility of "tails"; and considering no other outcomes are viable, the opportunity of either "heads" or "tails" is half off (which can additionally be written as 0.5 or 50%).
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Given: ABCD is a parallelogram.
Prove: AE
EC.
Step
1
try
Statement
ABCD is a parallelogram
Type of Statement
Reason
Given
Answer:
find it using angles
Step-by-step explanation:
Angle ABC is a straight angle.
Angles ABD and DBC are right angles.
Angles CBE and DBE are acute angles.
Angle ABE is an obtuse angle.
Angles
The sum of the three angles in any triangle is always 180°.
a + b + c = 180°
Knowing that the sum of the angles of triangle is 180° can help you to solve problems about triangles.
Angles
In this triangle, angle b is a right angle and angle c = 40°. What is the measure of angle a?
a + b + c = 180°
Since b is a right angle, b = 90°.
The problem states that c = 40°.
Therefore, a + 90° + 40° = 180°
a + 130° = 180°
a + 130° − 130° = 180° − 130°
a = 50°
Angle a measures 50°.
Angles
Click on the figure that matches this description.
An obtuse angle
Question 1 of 8
This is an acute angle. It measures less than 90°. Try again
This is a right angle. The square in the corner shows that it measures 90°. Try again
This is a straight angle. It measures 180°. Try again.
This angle is obtuse. It is greater than 90° and less than 180°.
One of these figures is an obtuse angle. Try again.
An obtuse angle is larger then a right angle and smaller then a straight angle.
Angles
Click on the figure that matches this description.
An acute angle
Question 2 of 8
This is an acute angle. It measures less than 90°.
This is a right angle. The square in the corner shows that it measures 90°. Try again
This is a straight angle. It measures 180°. Try again.
This angle is obtuse. It is greater than 90° and less than 180°. Try again.
One of these figures is an acute angle. Try again.
An acute angle is smaller then a right angle.
Angles
Click on the figure that matches this description.
A right angle
Question 3 of 8
This is an acute angle. It measures less than 90°. Try again
This is a straight angle. It measures 180°. Try again.
This angle is an obtuse angle. It measures more than 90° and less than 180°. Try again.
This is an acute angle. It measures less than 90°. Try again.
A right angle looks like a square corner and measures 90°.
A right angle measures 90°.
Angles
There are five question remaining. In each of these question, you will be asked to find the size of a missing angle.
Angles
Click on the correct answer.
Angle ABC is a right angle. If angle n is 40°, how large is angle m?
50°
140°
90°
60°
None of these
Question 4 of 8
90° − 40° = 50°
Angle m is 50°.
Angle ABC is 90° , and angle m is only part of this right angle. It is less than 90°. Try again.
Angle ABC is 90°, and angle m is only part of this right angle. Try again.
Angle m and n together from a 90° angle. Subtract 40° from 90° .Try again.
One of these is size of angle m. Try again.
Since angle ABC is a straight angle, angle m + angle n = 90°.
An object is moving at a speed of 6 inches every 4 to 5 days. express the speed in yards per year. round your answer to the nearest 10th
Answer:
The speed in yards per year is 60.8.
Step-by-step explanation:
To convert the speed from inches per day to yards per year, we need to first convert the speed to inches per year and then convert the units to yards per year.
First, we can convert the speed to inches per year by multiplying the speed by the number of days in a year:
Speed (inches/day) * Days per year = Speed (inches/year)
6 inches/day * 365 days/year = 2190 inches/year
Next, we can convert the units to yards per year by dividing the speed in inches per year by the number of inches per yard:
Speed (inches/year) / Inches per yard = Speed (yards/year)
2190 inches/year / 36 inches/yard = 60.8 yards/year
Rounding to the nearest 10th, we have:
60.8 yards/year ≈ 60.8 yards/year
Therefore, the speed in yards per year is 60.8.
In the group of ordered pairs shown, the x-values are inputs and the y-values are outputs. Select all the statements that are true.
(2, 4), (6, 3), (5, 4), (7, 3), (8, 2)
not ur dad but try looking in asda might find him
please help by today
Step-by-step explanation:
the angle south-east of x is hard to read.
I assume this is 86 (but could be also 96).
remember, the sum of all angles in a triangle is always 180°.
and the intersection angles between 2 lines are the same in both sides of the lines. the only difference between above and below angles is that they are left-right mirrored.
so,
180 = x + 22 + 86
x = 180 - 22 - 86 = 72°
x and y are intersection angles of 2 lines and are therefore equal (due to the left-right mirroring).
y = x = 72°
180 = w + 33 + 72
w = 180 - 33 - 72 = 75°
remember also that the sum of all angles around a single point on one side of a line is always 180°, because the line can be seen as diameter of a circle with the point being the circle center. and the degrees of a half-circle are 180°.
180 = angle1 + unnamed angle = angle1 + 85
angle1 = 180 - 85 = 95°
180 = angle2 + angle3 + unnamed angle =
= 42 + angle3 + 85
angle3 = 180 - 42 - 85 = 53°
for the third question we don't see a picture of the situation. I assume this is a circle with O being the center of the circle, and Q, N, P are points on the circle arc.
it is not clear, if the angle QOP is part of the angle QON, or if they are separate segments of the circle.
if the angle QOP is part of the angle QON, then the angle PON = 142 - 46 = 96°
if the angle QOP is separate from the angle QON, then the angle PON = 360 - 142 - 46 = 172°
Given function g on the graph, what is the domain of this function?
A part of linear function g is graphed on the grid
Answer: -7[tex]\leq[/tex]x[tex]\leq[/tex]6
5 3/5÷2 2/3 in its simpilest form
Answer: 2.1
Step-by-step explanation:
Calculator
If g (n +1) = g (n) +6 and g (1)=-25 then g (26)=?
(1) 131
(2) 125
(3) 54
(4) -19
Answer:
(2) 125---------------------------
Given is an AP with:
The first term of - 25,Common difference of 6.Use the explicit rule to find the 26th term:
t(n) = t + (n - 1)d, where t- the first term and d - common differenceg(n) = - 25 + 6(n - 1) = - 25 + 6n - 6 = 6n - 31g(26) = 6*26 - 31 = 156 - 31 = 125Correct choice is (2).
what is the probablity that six consecutive integers will be chosen as the winning lottery numbers where each number chsoen is an integer between 1 and 40
The probability is 0.00000911843.
The number of terms is 40 because the number selected falls within the range of integers 1 through 40 (inclusive).
Thus; n = 40
The combination formula, which is; gives the probability that 6 integers (r = 6)—the number of possible outcomes—will be obtained without repetition.
C(n, r) = n!/((n - r)!(n - r)!)
C(40, 6) = 40!/(6!(40 - 6)!)
C(40,6) = 3838380
When it comes to selecting a single item, there are several options available.
(1 - 6, 2 - 7, 8 - 13,...e.t.c)
There will be 35 successful results in all.
The likelihood that the winning numbers will be chosen from a set of six consecutive integers is;
P (that six consecutive integers will be chosen at random as the winning numbers) = likelihood of favorable outcomes/probabilities = 35/3838380 = 0.00000911843
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Show your work below in solving the equation
3^x-7=4
give the exact answer do not approximate
Answer:
x= 2.18265833
Step-by-step explanation:
is this for solve for x, because i got decimal if it was solve for x
3^x=4+7
3^x=11
In (3^x)=In (11)
xIn(3)=In (11)
x= In (11)/ In (3) Divide
X= 2.18265833
sets.
6. Which of the following BEST completes the
statement: "Net Income is a measure of..."
[A] the overall decrease in wealth over a period
and can be calculated by subtracting gross
income from expenses.
[B] the overall increase in expenses.
[C] the overall increase in liabilities over a period
and can be calculated by subtracting income
from expenses.
[D] the overall increase in wealth over a period
and can be calculated by subtracting expenses
from gross income.
[E] the overall decrease in expenses.
Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.
Option D is the correct answer.
What is net income?Net income is the amount remaining after deducting the expenses from the revenue collected.
We have,
Consider,
Amount collected after production of items = $400
Cost of production of the items = $250
Net income.
= Amount collected - Cost of production
= 400 - 250
= $150
Thus,
Net income is the overall increase in wealth over a period and can be calculated by subtracting expenses.
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Inez heard that a a general rule, he hould pend no more than 30% of her take-home pay on rent. If Inez' take-home pay i $46. 800 per year, what i the maximum amount per month that he hould pent or rent?
The maximum amount per month that Inez would spent on rent is $1170 knowing that he could spend no more than 30% of the take home pay.
Here Inez heard that a a general rule, he should pend no more than 30% of her take-home pay on rent. If Inez' take-home pay i $46. 800 per year.
The term Take-home pay is the net amount of income received after the deduction of taxes, benefits, and voluntary contributions from a paycheck. It is the difference resulting from the subtraction of all deductions from gross income.
Pay = $46,800
Total allowed = 46,800 x 0.30
Total allowed = $14,040
Now since we know that there are 12 months in a year, we need to divide the Total allowed by 12 to find how much Inez can pay in rent per month.
14,040 / 12 = $1,170
Following the rule that he could not spend more than certain of the take home pay he should rent $1170.
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when the students divide 65.8 by 13, their calculator tells them 5.0615384615. what value should the students report for the density, according to a strict application of the rules for use of significant figures?
Answer:
5.1
Step-by-step explanation:
When dividing or multiplying numbers, the answer should have the same amount of significant figures as the number in the problem with the least amount of sig figs.
In the problem 65.8 ÷ 13 ...
65.8 has 3 sig figs
13 has 2 sig figs
13 has THE LEAST AMOUNT OF SIGNIFICANT FIGURES
So, this means the answer must have the same number of sig figs as 13.
Let's round 5.0615384615 to TWO significant figures
the 6 in the number must be rounded up!
Final answer: 5.1
5.1 has TWO sig figs like the number 13
what two terms are used to refer to a search in which each value in a sequence is examined until a target value is found or the end of the sequence is reached?
This problem can be solved using divide and conquer techniques. An method known as "divide and conquer" works by breaking down a large task into smaller ones.
An algorithmic pattern is known as Divide and Conquer. In algorithmic approaches, the idea is to take a dispute involving a large amount of input, divide the input into smaller pieces, solve the problem on each of the smaller pieces, and then combine the piecewise solutions into a comprehensive solution. The Divide and Conquer is the algorithmic name of the approach that was used to solve the issue.
The three steps below are used in a dispute utilizing the Divide and Conquer method.
Create a group of subproblems from the main issue.
Conquer: Recursively and individually solve each subproblem.
Combine: Combine the solutions to the individual subproblems to arrive at the overall solution.
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2. Which of the following best represents the
range of the function?
a. All real numbers.
b. y ≤ 3
c. y = 3
d. x ≤ 3
3/5 + 7/8simplify where possible
59/40
The numerators don't line up. We require a connecting factor. Therefore, we multiply both denominators next. The next step is to multiply each numerator by the denominator of the other term.
As a result, we multiply 3 by 8 to get 24 and multiply 7 by 5 to get 35 and then 5 by 8 to get 40.
3/5=3*8/5*8 and 7/5= 7*5/8*5
We can add the numerators because our denominators are same.
24 + 35 = 59
As a result, we have the sum, which is
59/40
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Line k has a slope of 1/3. Line j is perpendicular to line k and passes through the point (1,4). Create an equation for line j.
keeping in mind that perpendicular lines have negative reciprocal slopes, and that line "k" has a slope of 1/3, then
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{1}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{1}\implies -3}}[/tex]
so for line "j" we're really looking for the equation of a line whose slope is -3 and that it passes through (1 , 4)
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- 3}(x-\stackrel{x_1}{1}) \\\\\\ y-4=-3x+3\implies {\Large \begin{array}{llll} y=-3x+7 \end{array}}[/tex]
3. the letters r, x, b, and q are all a. syllables. b. consonants. c. accented. d. vowels.
The given letters r, x, b, and q are all (B) consonants.
What are consonants?A speaking sound that is not a vowel is called a consonant.
It also refers to the alphabetic letters that stand in for certain sounds; consonants include Z, B, T, G, and H.
A consonant is a speech sound that is produced by the vocal tract closing completely or partially, according to articulatory phonetics.
Examples include the letters "p" and "b," which are pronounced with the lips, "t" and "d," which are pronounced with the front of the tongue, "k" and "g," which are pronounced with the back of the tongue, "h," which is pronounced in the throat, "f," "v," and "s," which are pronounced by forcing air through a narrow channel, and "m" and "n," which are pronounced with air flowing through the nose (nasals).
Vowels contrast with consonants.
Therefore, the given letters r, x, b, and q are all (B) consonants.
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Correct question:
The letters r, x, b, and q are all __.
a. syllables.
b. consonants.
c. accented.
d. vowels.
The dimensions of a rectangle are StartRoot 50 a cubed b squared EndRoot and StartRoot 200 a cubed EndRoot. A student found the perimeter as follows: 2 StartRoot 50 a cubed b squared EndRoot + StartRoot 200 a cubed EndRoot = 2 times 5 a b StartRoot 2 a EndRoot times 10 a StartRoot 2 a EndRoot. = 10 a b StartRoot 2 a EndRoot + 20 a StartRoot 2 a EndRoot. = 30 a b StartRoot 2 a EndRoot.
What is the student’s error?
The student should not have multiplied each expression by two.
The student simplified incorrectly.
The student simplified incorrectly.
The student incorrectly simplified
The correction made by the student is incorrect simplification of 30ab√2a+20a√2a
What is perimeter?The perimeter of a polygon is the sum of its, all the side lengths.
Given that, the dimension of a rectangle is given by, √50a³b² and √200a³
The perimeter of the rectangle is = 2(length + width)
Solving for the perimeter,
2(√50a³b²+√200a³)
= 2(5ab√2a+10a√2a)
= 10ab√2a+20a√2a
The student solved it as 30ab√2a,
Which is incorrect, because 'b' is not there in both the expressions, hence, we cannot add them.
Hence, The correction made by the student is incorrect simplification of 30ab√2a+20a√2a
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According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you can assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less that the overall mean waiting time of 13 minutes? Use alpha=0.05
- Establish the two hypotheses
- Calculate the test statistic
- Make a decision using the critical value approach
- Make a decision using the p-value approach
We can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.
Two-Hypotheses:
H0: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is not significantly less than the overall mean waiting time of 13 minutes.
Ha: The mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.
Test Statistic: t = (11 - 13) / (8/√50) = -2.5 and the Critical Value Approach is: The critical value for a one-tailed test at alpha = 0.05 is 1.645. Since the test statistic (-2.5) is less than the critical value (1.645), we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes, and the P-Value Approach: The p-value for the one-tailed test is 0.0062. Since this p-value is less than alpha = 0.05, we can reject the null hypothesis and conclude that the mean waiting time for calls placed during the first 30 minutes the IRS helpline is open each day is significantly less than the overall mean waiting time of 13 minutes.
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Find the coordinates of the zeros and the vertex in order to graph the parabola represented by the
equation y = -(x - 1)(x - 5).
Answer:
Step-by-step explanation:
y = (-x+1)(x-5)
zeroes
(-x+1)(x-5) = 0
-x + 1 = 0
x = 1
(1,0)
x -5 = 0
x = 5
(5,0)
Vertex
y = (-x+1)(x-5)
y = -x²+5x + x - 5
y = -x² + 6x - 5
x coordinate
-6/-2
3
y coordinate
-(3)² + 6(3) - 5
-9 + 18 - 5
- 14 + 18
4
V(3,4)
mason stands on the 5^\text{th}5 th 5, start superscript, start text, t, h, end text, end superscript step of a vertical ladder. the ladder has 151515 steps, and the height difference between consecutive steps is 0.5\text{ m}0.5 m0, point, 5, start text, space, m, end text. h(n)h(n)h, (, n, )models the height above the ground of mason's feet (in \text{m}mstart text, m, end text) after moving nnn steps (if mason went down the ladder, nnn is negative.) which number type is more appropriate for the domain of hhh?
Since the stages are simply whole values taken one after the other, they should be whole numbers or integers.
What in mathematics is a whole number?
Complete numbers those figures that contain zero and natural integers. not a decimal or fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. a negative number, zero, or a counting number. Whole numbers are made up of all the ordinal numbers and 0.
Natural numbers are the term used to describe counting numbers in mathematics. Therefore, the whole number can be described as a combination of all natural numbers and 0. Along with zero, all positive integers are also considered whole numbers.
He is currently on step 5, there are 15 steps total, therefore he is actually 10 steps away from the top of the ladder. If we walk down the ladder with N being negative, he is -5 steps from the ground.
{ N | N ∈ ℤ , -5 ⩽ N ⩽ 10 }
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Line m passes through points (7, 6) and (5, 13). Line n is perpendicular to m. What is the
slope of line n?
Answer:
-3.5
Step-by-step explanation:
To find the slope of line n, we need to find the slope of line m first. The slope of a line is calculated by dividing the difference in the y-coordinates of two points on the line by the difference in the x-coordinates of the same two points. In this case, we can use the two points (7, 6) and (5, 13) to calculate the slope of line m. The difference in the y-coordinates of these two points is 13 - 6 = 7, and the difference in the x-coordinates is 5 - 7 = -2. Dividing the difference in the y-coordinates by the difference in the x-coordinates yields 7 / -2 = -3.5.
A line is perpendicular to another line if the product of their slopes is -1. Since the slope of line m is -3.5, the slope of line n, which is perpendicular to line m, is -1 / -3.5 = 1/3.5 = <<-1/-3.5=1/3.5>>1/3.5.
Answer:
Slope of a line equation.
Formula for slope of line n is m= rise/run. y2-y1/x2-x1
(7,6) is (x1, y1) and (5,13) is (x2,y2). Simply plug these values in to the equation and solve.
Step-by-step explanation:
(13)-(6) = 7.
(5)-(7) = -2.
7/-2 = - 7/2
- 7/2 = -3.5.
Perpendicular just means that the 1. answer changes sign (pos/neg). This answer is negative, so it becomes a positive. 2. the denominator number switches places with the numerator number. so 7/2 becomes 2/7. Decimal version is 3.5/1 becomes 1/3.5
Final Answer: 1/3.5 or 2/7
What number must multiply each side of the equation to produce the equivalent equation
x = -80
The number must multiply each side of the equation to produce the equivalent equation is -5/3.
What is an equivalent equation?Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation. An equation is equivalent if both sides are multiplied or divided by the same non-zero value.
The given equation is -3/5 x= 48
Multiply each side of the equation by -5/3, we get
[tex]\frac{-3x}{5} \times\frac{-5}{3} =48\times(\frac{-5}{3} )[/tex]
x=-80
Therefore, the number must multiply each side of the equation to produce the equivalent equation is -5/3.
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"Your question is incomplete, probably the complete question/missing part is:"
What number must multiply each side of the equation -3/5 x= 48 to produce the equivalent equation x= -80?