He will cover total 247.5 kilometers on day 30 of his programe .
What is arithmetic progression ?When there are identical differences between every two next words, the series is known as an arithmetic progression (AP). There is a chance to find a formula for the nth term of the AP using this kind of development. The series 2, 6, 10, 14, etc., for instance, is an example of an arithmetic progression (AP) because it follows a pattern in which each number is acquired by adding 4 to the preceding word. Nth term in this series equals 4n-2.
Given that :Lerato begins a new cycling programme with 2 km on the first day. Each day, he will increase his cycling by 500 m.
The formula to find Sum of an arithmetic progression is
S = [tex]\frac{n}{2}[2a+(n-1)d][/tex]
here , a = 2km
n = 30
d = 0.5km
S =[tex]\frac{30}{2}[2(2)+(30-1)0.5][/tex]
S = 247.5 km
He will cover total 247.5 kilometers on day 30 of his programe
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Bill has 5 apples and 5 bananas. He can put only 5 pieces of fruit in a bowl.
Will the number of bananas be greater or less as you move down the table? How do you know?
Answer:
Varies
Step-by-step explanation:
If bill were to put 4 bananas and only 1 apple there would be more banana's then apples, but if he put more apples then bananas then it would be the greater then bananas
Help with number three
The table shows that each output(y) is obtained by multiplying each input(x) value by 2.
[tex]\begin{gathered} x\cdot2=y \\ 5\cdot2=10 \\ 7\cdot2=14 \\ 9\cdot2=18 \end{gathered}[/tex]Thus, an equation for the given multiplicative relationship is:
[tex]y=2x[/tex]A large box of spaghetti noodles contains 3 pounds and costs $2.40. A student said the unit cost is $1.20 per pound. Is the student correct? Explain.
The cost of 3 pounds =$2.40
For the cost of 1 pound, divide the cost of three pounds noodles with 3.
[tex]\begin{gathered} Cost\text{ of 1 pound noodles=}\frac{2.40}{3} \\ \text{Cost of 1 pound noodles=\$0.8} \end{gathered}[/tex]The student is not correct ,
The cost of unit pound is $0.8
리 20 Use the figure below to determine the measures of the following angles. 21 X 42 35) m 21 - 36) m 22
I need help please!
Solving the Question
We're only given one angle: the angle that measures 35°.
This angle and ∠1 are supplementary angles, meaning they add up to 180°. To find ∠1, subtract 35 from 180:
180 - 35 = 145°
The angle and ∠2 are corresponding angles, meaning they are on the same sides of the diagonal line and the transversal.
Corresponding angles are always equal.
Therefore, ∠2 = 35°.
Answer∠1 = 145°
∠2 = 35°
In the right-angled triangle ABC in Fig. 4.3, B = 90° and the lengths of AB and BC are given to the nearest centimetre. Calculate AC.
Answer:
|AC| = 132 cm (nearest centimetre)
Step-by-step explanation:
Pythagoras Theorem
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The formula is:
[tex]\large\boxed{c^2=a^2+b^2}[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangle.From inspection of the given right triangle:
a = AB = 45 cmb = BC = 124 cmc = ACSubstitute the given values into the formula and solve for AC:
[tex]\begin{aligned}c^2 & = a^2+b^2 &\\\\\implies AC^2&=AB^2+BC^2\\ AC^2&=45^2+124^2\\ AC^2&=2025+15376 \\ AC^2&=17401\\\sqrt{ AC^2}&=\sqrt{ 17401}\\ AC&=131.91285\\AC&=132\; \sf cm \; (nearest\;centimetre)\end{aligned}[/tex]
Therefore, |AC| is 132 cm to the nearest centimetre.
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rate r
P= $5000.00, A = $6250.00, t= 5 years
Simple interest typically favors consumers who pay their bills or loans on time or early each month because it is frequently calculated on a daily basis. The loan's simple interest rate is 4.5%.
Who benefits from a simple interest loan?Simple interest typically favors consumers who pay their bills or loans on time or early each month because it is frequently calculated on a daily basis.
In the aforementioned student loan example, if you paid a $300 payment on May 1st, $238.36 would be applied to the principle. On April 20, if you made the same payment, $258.91 would be applied to the principal. Your main balance will decrease more quickly and the loan will be paid off faster than anticipated if you can make an early payment every month.
On the other hand, if you pay the loan back late, you pay more in interest than if you pay it on time. If your payment is due on May 1 and you make it on May 16 (using the same car loan example), you will be charged interest for 45 days at a cost of $92.46. Consequently, only $207.54 of your $300 payment is applied to the principal. If you frequently make late payments over the course of a loan, your final payment will be more than anticipated because the principal did not decrease at the anticipated rate.
Principal amount,
P=$5000
Future value,
A=$5900
Time,
t=4years
Let us determine the loan's simple interest rate:
A=P(1+rt)
5900=5000(1+r*4)
5900=5000(1+4r)
5900=5000*1+5000*4r
5900=5000+20000r
5900−5000=20000r
900=20000r
20000r=900
r=900/20000
r=9/200
r=0.045
r=0.045/100%
r=4.5%
Therefore, the loan's simple interest rate is 4.5%.
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find volume of this figure . round to the nearest hundredth and use 3.14 for pie
ANSWER:
2034.72 cubic units
STEP-BY-STEP EXPLANATION:
The volume of the cylinder is given by the following equation;
[tex]V=\pi\cdot r^2\cdot h[/tex]The radius is equal to 6 and the height is equal to 18, let's substitute them and calculate the volume of the shown cylinder, like this:
[tex]\begin{gathered} V=3.14\cdot(6)^2^\cdot(18) \\ \\ V=3.14\cdot36\cdot18 \\ \\ V=2034.72 \end{gathered}[/tex]The volume of cylinder is equal to 2034.72 cubic units
Help it’s timed!!!
I have no idea how to solve please help
Answer:
Here is the answer: sin(3π/2) = -1
So 3π/2 is the correct choice.
a box shaped as a cube has an edge of 13 inches. if a kickball with a diameter of 11 inches is placed inside of it how much of the space is not filled?(to the nearest cubic inch)
we get that the volume of each object is
[tex]\begin{gathered} V_{\text{box}}=13^3=2197 \\ V_{\text{ball}}=\frac{4}{3}\cdot\pi\cdot(5.5)^3\approx696.90997032\approx697 \end{gathered}[/tex]so the reamining space is:
[tex]2197-697=1500[/tex]A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 58
5 52
7 48
10 42
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 62 through the point 1 comma 60
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 62 through the point 1 comma 59
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
The linear equation relating the given condition is y + 10x - 62 = 0 .
Each solution in the scenario with two variables can be understood as the Cartesian coordinate system of such a point on the Euclidean plane.
A line in the Euclidean space is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from. In the Euclidean space of dimension n, the equations of a linear equation with n variables generate a hyperplane (a subset of dimension n 1).Let the linear relation between the two variables be given by y=mx + c
Now we put the values to get the constants.
58 = 2m + c
52 = 5m + c
solving we get :
52 - 5m = 58 - 2m
or, -6 = 3m
or, m = -2
Now we put those values in the equations
52 = 5m + c
or, 52 = -10 + c
or, c = 62
The equation relating the sunglasses is y + 10x - 62 = 0 .
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Answer: it's A if ur on that question six flvs question counting that was so hardddddddddddddddddddddddddddd
Step-by-step explanation:
Evalúe the limit. Show steps
After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow \Pi }cos(x)[/tex] as x approaches π is –1
What is limit?As an input or as an index approaches a specific value in mathematics, a limit is the value that the function, sequence, or index approaches. The definitions of continuity, derivatives, and integrals all require limits, which are fundamental to calculus and mathematical analysis.
In addition to having a connection to the category theory concepts of limit and direct limit, the idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network.
A limit of a function is typically expressed in formulas as
[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]
To find the limit
⇒ [tex]\lim_{x\rightarrow \Pi }cos(x)[/tex]
Evalúe π as x
= cos (π)
= cos 180°
= cos(180° – 0°)
= – cos 0°
= – (1)
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1) A manufacturing unit produced 112, 336 and 1008 Easter baskets on days one,
two and three. If the unit continues to manufacture baskets at the same rate,
how many baskets will it produce on the 4th, 5th and 6th day respectively?
There are 3024, 9072 and 27216 baskets are produced in 4th, 5th and 6th days respectively.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A manufacturing unit produced 112, 336 and 1008 Easter baskets on days one, two and three.
Now,
On first day, there are 112 baskets.
And, On second day, there are 336 baskets.
So, Clearly 112 x 3 = 336
That's mean every day the number of produce baskets are three times the previous day.
So, On fourth day;
Number of Easter basket produce = 1008 x 3 = 3,024
On fifth day;
Number of Easter basket produce = 3,024 x 3 = 9,072
On sixth day;
Number of Easter basket produce = 9,072 x 3 = 27,216
Thus, There are 3024, 9072 and 27216 Easter baskets are produced in 4th, 5th and 6th days respectively.
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Complete the following equation using <, >, or = 120%___1
The answer to the expression 120% (_____) 1 is:
120% > 1. See the explanation related to the percentage problem below.
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently indicated by the percent symbol, "%."
To overcome the above problem, we must transform the two numbers into the same form.
Because adding zeroes to the ending of a decimal does not modify the value, we know that 1 = 1.00.
To convert a decimal to a percentage, multiply it by 100 and add a percent sign.
1.00 * 100 = 100%
Hence, 1 = 100%
Because 120% is greater than 100%, it is right, therefore, to state that:
120% > 1
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Is the list of no. 3,9,15,21 ........ From an Ap
The given list of numbers 3,9,15,21..form an Arithmetic Progression(AP).
What is Arithmetic Progression?A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A fixed number is added to the term preceding it in the sequence to obtain each term, with the exception of the initial term.
Given list of numbers is 3,9,15,21 ...
To determine whether the series is an Arithmetic Progression, find the difference of the terms which should be constant in an AP.
9 - 3 = 6
15 - 9 = 6
21 - 15 = 6
Therefore, as each term of the given series differs from its preceding term by 6 it is an AP.
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15. Choose the correct answer for this problem:
1/7 x ?
Thank you!
The required fraction is 1/14.
What is fraction?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.
For illustration: There are five kids in all.
Five in three are female. So, three-fifths of the population are girls.
Of the 5, two are boys. So, two-fifths of the population are boys.
As in this question 1 out of the 2 boxes are shaded.
Thus the required fraction is 1/2
Thus the required number is [tex]\frac{1}{7}[/tex]×[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{14}[/tex].
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x3 =x2 (?)
I dentify the missing factor!!!!!
The missing factor in the given expression x³ = x²(?) is; x
How to solve laws of exponents?
The laws of exponents are;
1) When multiplying like bases, keep the base the same and add the exponents.
2) When raising a base with a power to another power, keep the base the same and multiply the exponents.
3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.
Now, we are given the expression;
x³ = x²(?)
The question mark indicates a missing term. Thus, we will use division property of equality to divide both sides by x² to get;
x³/x² = x
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can yall help with this pls and ty
Answer:
4 1/3
Step-by-step explanation:
I believe it is 4 1/3 because all the other ones like 9=3 and 12=4 are divided by 3 so if you divide 14 by 3 you get 4 1/3 as your answer.
Express the confidence interval (78.5,154.7) in the form of ¯x± ME (Error Bound).
The expression of the confidence interval (78.5, 154.7) in the form of x¯ ± ME is; CI = 116.6 ± 38.1
How to find the Confidence Interval?
We are given the confidence interval as;
CI = (78.5, 154.7)
Now, we want to express the given confidence interval in the error bound form which is; x¯ ± ME
where;
x¯ is sample mean
ME is margin of error
Now, the boundaries of the interval as two points is the midpoint between them which would be (78.5 + 154.7)/2 = 116.6.
This is right in the middle of 78.5 and 154.7.
This value of 116.6 is the sample mean represented by x¯, since x¯ is in the middle of the interval. This means that 78.5 and 154.7 are the same distance (the margin of error, ME) away from 116.6. .
116.6 - 78.5 = 38.1 and 154.7 - 116.6 = 38.1
Thus, the expression is;
CI = 116.6 ± 38.1
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Graph the function by first finding the relative extrema. f(x) = x + 4x2 - X-4 O 2 O I need help with this.
The equation is:
[tex]f(x)=x^3+4x^2-x-4[/tex]So to know that, we can find the intercept in the y axis by replacing x=0 so:
[tex]\begin{gathered} y=0^3+4(0)^2-0-4 \\ y=-4 \end{gathered}[/tex]So if you see the functions the only one that intercept the y axis in -4, then the solution is option (D)
If a and b are integers such that -6 ≤ a ≤ 3 and -4 ≤ b < 5, what is the least possible value of a times b?
SOLUTION
From the question, it means that
[tex]\begin{gathered} a=-6,-5,-4\text{ . . . . . .3} \\ b=-4,-3,-2\text{ .. .. . . . . .4} \end{gathered}[/tex]The least possible value of a and will be a ngative number, gotten by multiplying a negative value by a positive value. So this should be
the smallest value of a, that is the -6 multiplied by the biggest value of b = 4
[tex]-6\times4=-24[/tex]Hence the answer is -24
Please help I’ll mark you as brainliest if correct!!!
1) A local company has a fixed cost of$45,507.00 each vear, and $34,614.00 foreachperson employed for the yearNext year, the company projects thatcosts will total $2.817,027.00. Whichequation below could be used todetermine how many people thecompany intends to employ next yearA. 2.817,027 = 34,644p + 45,507B. 2,817,027 = 45,507p +34 644C. 2,817,027 = 34,644p --- 45,507D. 2,817,027 = 34,644(p+ 45,507)
we have the following:
[tex]\begin{gathered} \text{total cost}=\text{variable cost + fixed cost } \\ $2817027=$34644\cdot p+45507 \end{gathered}[/tex]therefore, the answer is the first option
What is the slope of the line through (-9,6) and (-3,9)? Choose 1 answer: A 2 B 1 2 1 2 D -2
The slope according to the given points of line is (B) m = 1/2.
What do we mean by slope?Slope, the inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run"). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope.So, points are: (-9,6) and (-3,9)
Slope formula: m = (y₂ - y₁)/(x₂ - x₁)Now, substitute the values in the formula as follows:
m = (y₂ - y₁)/(x₂ - x₁)m = (9 - 6)/((-3) - (-9))m = (9 - 6)/((-3) + 9))m = 3/6m = 1/2Therefore, the slope according to the given points of the line is (B) m = 1/2.
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The correct question is given below:
What is the slope of the line through (-9,6) and (-3,9)? Choose 1 answer:
A. 2
B. 1/2
C. -1/2
D. -2
Write this equation in standard form.
x^2+y^2-6x-6y+2=0
Show work.
The equation in standard form is mathematically given as
[tex](x-3)^2 +(y-3)^2 = 4^2[/tex]
This is further explained below.
What is a standard form.?Generally, A mathematical notion, such as an equation, number, or expression, maybe written down in a form called a standard form, which is a form that adheres to a predetermined set of guidelines.
The standard form is used if a condensed representation of a very big or very tiny number is required.
For instance, the number 4.5 billion years is represented by the numeral 4,500,000,000.
In conclusion,
[tex]x^2 + y^ 2- 6x-6y+2=0[/tex]
Therefore
[tex](x^2 - 6x) +(y^2-6y) +2 =0\\\\(x^2 - 2(3)x +3^2) -3^2 + (y^2 - 2(3)y +3^2) -3^2+2 = 0\\\\(x-3)^2 +(y-3)^2 = 4^2[/tex]
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Solve the equation on the interval 0≤x < 2.
2
4 tan²x - 12 = 0
Answer:
8 sec^2 x + 4 tan^2 x − 12 = 0 → sec^2x = tan^2x + 1
8 [ tan^2x + 1] + 4tan^2x - 12 = 0
8tan^2x + 8 + 4tan^2x - 12 = 0
12tan^2x - 4 = 0 divide through by 4
3tan^2x - 1 = 0
3tan^2x = 1
tan^2x = 1/3 take the square root of both sides
tanx = ±1 / √
The surface of a city playground is being covered with rubber mulch, which is shredded rubber made from recycled tires. A city worker measures the dimensions of the playground as shown. The recommended depth of the mulch is 4 inches. A 1-ton bag of mulch contains about 3 cubic yards of mulch. How many bags of mulch are needed to cover the surface of the playground?
The width is 40.5 and the Length is 66.75
The number of bags of mulch that is needed to cover the playground is 3,605 bags.
How many bags of mulch is needed?The first step is to determine the volume of the surface of the city playground. The volume is the product of the length, width and height of the playground.
Volume = length x width x height
4 x 40.5 x 66.75 = 10,813.50 inches³
The second step is to determine the number of bags of mulch that is needed to cover the surface of the playground.
Number of bags of mulch = volume of the playground / volume one bag can cover
10,813.50 inches³ / 3 = 3,604.5 bags ≈ 3,605 bags
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A certain star is 4.1 × 10² light years from the Earth. One light year is about 5.9 × 10¹² miles. How far from the earth (in miles) is the star?
Answer:
=24.19×10^14
Step-by-step explanation:
we will just all add to get the distance
=4.1×10²×5.9×10¹²
=4.1×5.9×10²×10¹²
=24.19×10^14
Liar, liar! From experience, we know that a certain lie detector will show a positive
reading (indicating a lie) 10% of the time when a person is telling the truth. Suppose that
a random sample of 5 suspects is subjected to a lie detector test. Find the probabil-ity of
observing no positive readings if all suspects are telling the truth.
Probability is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
The probability of observing no positive reading if all the subjects are telling the truth is 9/10.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Positive reading when telling the truth = 10%
No positive reading when telling the truth = 90%
The probability of observing no positive reading if all the subjects are telling the truth
= 90%
= 90/100
= 9/10
Thus,
The probability of observing no positive reading if all the subject are telling the truth is 9/10.
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Say you are given the graph of the line y = -x.
Write the equation of the line that is perpendicular to the given line and goes through
the point (8, 2).
The equation of the line which is perpendicular and goes through the point (8,2) is slope-intercept form of y = x - 6.
What is slope-intercept form?
A line's equation can be written in the slope-intercept form such that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are instantly visible. This form is commonly referred to as the y = mx + b form.The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6
The equation of the required line in slope-intercept form is expressed as:
y-y0 = m(x-x0) where:
m is the slope
(x0, y0) is the point on the lin
Given the equation of the line as y = -x
Get the slope of the line
mx = -x
m = -1
Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))
y-y0 = m(x-x0)
y - 2 = 1(x-8)
y - 2 = x - 8
y = x - 8 + 2
y = x - 6
Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.
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f(x) = 2x - 1 g(x) = - 48 - 2 2 Find (f +g)(-3)
The value of the function is -9
What are functions?Functions are simply defined as mathematical expressions, rules, laws o theorem that compares or explains the relationship between two variables.
These variables are known as;
Independent variableDependent variableBased on the information given, we have that;
f(x) = 2x - 1 g(x) = - 4x - 2To determine the value of the function, (f +g)(-3), we have to add the functions for both f(x) and g(x)
We have;
(f +g)(x) = 2x - 1 + (-4x -2)
expand the bracket
(f +g)(x) = 2x - 1 - 4x - 2
Now, substitute the value of x as -3, we have;
(f +g)(-3) = 2(-3) - 1 - 4(-3) - 2
expand the bracket
(f +g)(-3) = -6 -1 + 12 - 2
Add or subtract the values
(f +g)(-3) = -9
Hence, the value is -9
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