Assuming simple interest, the formula to calculate the interest Ms. Paul paid is:
[tex]Interest=Principal\times Rate\times Time[/tex]In the problem, here are the given information:
Principal (Money borrowed) = $1,200
Rate = 18% or 0.18 in decimal form
Time = 9 months or 0.75 year.
(Take note that the time in the formula is measured in years.)
Let's plug in the given information to the interest formula above.
[tex]Interest=1,200\times0.18\times0.75[/tex]Then, solve.
[tex]Interest=162[/tex]Therefore, Ms. Paul paid interest of $162.
The graph represents the projected profits for a
company, y, based on the number of units sold, x.
250
200
150
100
50
0
10 15
20
(25, 200)
25
(30, 150)
30
35
x
If the end-of-year analysis indicates that profits did not
meet expectations, which inequality in vertex form
represents the region containing the results of the
year?
Oy< -2(x+25)² - 200
O y> 2(x-25)² + 200
y> 2(x+25)² - 200
Oy< -2(x-25)² + 200
The inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
From the graph:
The vertex is:
(25, 200)
The vertex form of the parabola:
y = a(x - h)² + k
y = a(x - 25)² + 200
Plug x = 30 and y = 150
a = --2
y = -2(x - 25)² + 200
The inequality will be:
y < -2(x - 25)² + 200
Thus, the inequality in vertex form represents the region containing the results of the year is y < -2(x - 25)² + 200 option (D) is correct.
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A 75 -inch pipe is cut into two pieces. One piece is two times the length of the other. Find the lengths of the two pieces.
Answer:
5 times the length of the short piece = 75 inches
The length of the short piece =75 / 5 = 15 inches
Length of the long piece = 4 times the length of the short piece = 60 inches
Check: 15 + 60 = 75 inches
yay
what are the transformations of this functions compared to the parent function
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.
Numerous different coordinate systems can be used to describe geometrical figures.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system. The coordinate transformation from polar to Cartesian coordinates is given by the formulas x = r cos and y = r sin, for example, if the polar axis is the positive x axis on the plane and the origins of the Cartesian coordinates (x, y) and polar coordinates (r) are the same.Every bijection from the space to itself can be related to two coordinate transformations.The formulas for the new coordinates of each point's image are constructed in a way that the old coordinates of the original point's image are maintained.In particular, the change of algebraic equations, it is a typical kind of algebraic problem.To learn more about transformation visit:
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Explain how -6 2/5 + 7/3
Answer is -4.0
Answer:
Answer is - 4 1/15
Step-by-step explanation:
-6 2/5 = -32/5
-32/5 + 7/3 to add fractions they must have the same denominator
- 96/15 + 35/15 = ( -96 + 35) / 15 = - 61/15 = - 4 1/15
The gas tank in Margaret's car holds 27 gallons of gas, and she starts out with a full tank. She
drives her car every day, and each day she uses an average of 1.3 gallons. How may gallons wil
she have left after 3 days?
Answer:
She will have 23.1 gallons left after 3 days.
Step-by-step explanation:
We know Margaret uses an average of 1.3 gallons of gas every day and her car holds 27 gallons total. In three days, she would use 3 times her daily average, or 3 * 1.3 = 3.9 gallons consumed in 3 days. To find how many gallons are left in her tank after 3 days, we would subtract 3.9 gallons from 27 gallons. This equals exactly 23.1 gallons of gas.
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
The powers can be used in the following manner using multiplicative identity.
Powers are mathematical expressions of the kind where x is the base and n is the exponent. In powers, the exponent specifies how many times to multiply the base by itself whereas the base is the integer or variable that is continuously multiplied.
The quotient rule states that exponents should be subtracted when dividing powers by the same base. For instance, h(6-2) Equals h when h(6) is divided by h(2) (4). Subtracting the exponents is a quick and easy way to simplify the issue.
When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. When separating similar words with exponents, using the Quotient of Powers Rule to minimize the number of terms. This rule states that when dividing words with the same base, the exponents should be removed in order to find the result. The trick is to eliminate only exponents with compatible bases.
Since the multiplicative identity, or one, is the simple outcome of no numbers at all, it follows that every integer raised to the power of zero equals one.
Thus, we came to the logical conclusions.
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school children shared oranges as follows .Jonas got 1/3 of the total and the remaining were shared between Mary and Rejoice in the ratio 3:2. if Rejoice got 24 oranges How many did Jonas get
The appropriate choice of ratio will be given by
Jonas got 30 oranges
What is ratio?
Ratio determines the comparision among many quantities with the same unit.
Here,
Let Mary got 3x oranges and Rejoice got 2x oranges
By the Problem,
[tex]2x = 24[/tex]
[tex]x = \frac{24}{2}[/tex]
[tex]x = 12[/tex]
Number of oranges Mary got = [tex]12 \times 3[/tex]
= [tex]36[/tex]
Number of oranges shared between Mary and Rejoice = [tex]24 + 36[/tex]
= [tex]60[/tex]
Fraction of oranges shared between Mary and Rejoice = [tex]1 - \frac{1}{3}[/tex]
= [tex]\frac{3 - 1}{3}[/tex]
= [tex]\frac{2}{3}[/tex]
Total number of oranges = [tex]\frac{60}{\frac{2}{3} }[/tex]
= [tex]60 \times \frac{3}{2}[/tex]
= [tex]90[/tex]
Number of oranges Jonas got = [tex]90 \times \frac{1}{3}[/tex]
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.) Arjen lives in Wisconsin. He said it was -10 degrees in the morning and it dropped 15degrees by midnight. What was the temperature at midnight?a. Show a mathematical statement to represent this situation and evaluate it.b. Write an inequality statement for -10 and 15 that uses the >< symbol.c. What is the absolute value of the morning temperature? Show a mathematicalstatement and evaluate it.
So,
The temperature was -10 degrees in the morning. Given that it dropped 15 degrees by midnight, we could substract 15 to -10 to find the temperature at midnight:
[tex]-10-15=-25[/tex]The temperature at midnight was -25 degrees.
b. Clearly,
[tex]-10<15[/tex]c. The absolute value of the morning temperature is:
[tex]|-10|=-(-10)=10[/tex]That's because:
[tex]undefined[/tex]5. A Gatorade recipe calls for 2 cups of mix for every 4 cups of water. If you
have 16 cups of water, how many cups of mix do you need?
A total of 8 cups of mix is needed for a Gatorade recipe calls for 2 cups of mix for every 4 cups of water if you have a total of 16 cups of water.
Unitary Method: What is it?The unitary technique in actuality involves first determining the actual value of a single unit, alongside followed by the value of the necessary number of units.
The unitary approach is a kind of a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
2 mix for 4 cups of water
⇒ 1 mix for 2 cups
⇒ for 1 cup = 1/2 mix
so for 16 cups = 8 mix
What is an example of a unitary method?A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.
The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
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A probability experiment consists of rolling a fair 15-sided die. Find the probability of the event below. rolling a number divisible by 3
Probability of an experiment consists of rolling a fair 15 -sided die with an event of rolling a number divisible by 3 is P(E)=(1 /3).
As given ,
Total number of outcomes of an experiment consists of rolling a fair 15-sided die 'n'
={1, 2, 3, …., 14, 15}
=15
Number of outcomes of an event 'E' showing rolling a number divisible by 3 'n(E)'
={3,6,9,12,15}
=5
Probability of event showing rolling a number divisible by 3 'P(E)'
=(Total number of favourable outcomes)/(Total number of outcomes)
=n(E)/n
= 5/15
=1/3
Therefore, probability of an experiment consists of rolling a fair 15 -sided die with an event of rolling a number divisible by 3 is P(E)=(1 /3).
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You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:
When you're reading a study that reports selecting a random sample of hospitals and estimating admission delay times, it's an example of C. probability sampling.
What is probability sampling?Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection. In general, probability sampling is more difficult, time-consuming, and expensive than non-probability sampling.
Using a method based on probability theory, probability sampling is a strategy in which the researcher selects samples from a larger population.
Researchers can produce a sample that accurately represents the relevant real-world population by using probability sampling.
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You are reading a study that reports selecting a random sample of hospitals and estimating admission delay times. You know this is an example of:
a. Quota sampling
b. Convenience Sampling
c. Probability sampling
d. Sampling bias
Does the frequency distribution appear to have a normal distribution using a strict interpretation of the relevant criteria?
Speed-- Number of cars
0-29 4
30-59 16
60-89 60
90-119 20
No, the distribution is not symmetric THIS ONE
No, the frequency do not increase from the low frequency to a maximum frequency
Yes, all the requirements are met
The verdict on whether the frequency distribution given appears to be normal is; No, the distribution is not symmetric.
What kind of frequency distribution is as given in the task content?It follows from the task content that it is required to determine if the frequency distribution as given appears to be normal.
On this note, since a major distinctive feature of a normal distribution is that; there is a concentration of frequency in the middle and additionally, a normal distribution infers symmetry in the frequency distribution.
Therefore, since none of the data values (speed) can be chosen as the middle value, and the distribution is not symmetric, it follows that;
The frequency distribution in discuss is not a normal distribution because the distribution is not symmetric.
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You want to open an account with $2,000. You can earn 4% interest each year, and you plan to leave this account for 6 years. How much more would the account be worth after 6 years by calculating interest compounded daily versus calculating simple interest? (Assume 365 days in a year.) Do not round until the final answer. Round to the nearest cent.
The account would be worth more after 6 years if calculating interest compounded daily versus calculating simple interest by $62.46
How to calculate compound interest and simple interest?Principal, p = $2,000Interest rate, r = 4% = 0.04Time, t = 6 yearsNumber of periods, n = 365 daysCompound interest:
A = P(1 + r/n)^nt
= 2,000(1 + 0.04/365)^(365×6)
= 2,000.00(1 + 0.000109589041095)^(2190)
= 2000(1.0.000109589041095)^2190
= 2000 (0.00010958904109589)
= $2,542.46 to the nearest cent
Simple interest:
S.I = principal × rate × time
= 2,000 × 0.04 × 6
= $480
Total = Principal + simple interest
= $2,000 + $480
= $2,480
To find the amount more would the account would be worth after 6 years by calculating interest compounded daily versus calculating simple interest
= Compound interest - Simple interest
= $2,542.46 - $2,480
= $62.46
In conclusion, the account would be worth $62.46 more if compounded daily than simple interest.
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Explain why when multiplying powers you add rather than multiply the exponents.Explain why when multiplying powers you add rather than multiply the exponents.
Jenny put all her shoeboxes in a row. The width of each shoebox is 12.02 cm. What is the total width of all 14 shoeboxes?
Answer:
168.28
Step-by-step explanation:
HELP! Alegbra 2
A soccer ball is kicked into the air so that its height, h, in feet, after t seconds is given by the function:
h(t)= -16t^2+96
What is the maximum height the ball reaches?
How long is the ball in the air?
The ball reaches a maximum height of 96 feet and it spent 0 seconds in the air
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the maximum height the ball reaches?The quadratic equation is given as
h(t) = -16t^2 + 96
Differentiate the equation of the function
So, we have
h'(t) = -32t
Set the differentiated function to 0
So, we have
-32t = 0
Divide both sides by -32
So, we have
t = 0
Substitute t = 0 in the equation h(t) = -16t^2 + 96
So, we have
h(0) = -16(0)^2 + 96
Evaluate
h(0) = 96
This means that the maximum height of the ball is 96 feet
How to determine the time spent in the air?Recall that the quadratic equation is given as
h(t) = -16t^2 + 96
Next, we differentiate the equation of the function
So, we have
h'(t) = -32t
Set the differentiated function to 0
So, we have
-32t = 0
Divide both sides by -32
So, we have
t = 0
Hence, the ball spent a total of 0 seconds in the air
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Zoe says that 2³ · 4² can be rewritten as 8⁶. Juana says that it can be rewritten as 8⁵. Danladi says that it cannot be rewritten as either of these expressions. Who is correct? Explain.
Answer:
Danladi is correct
Step-by-step explanation:
Danladi is correct because 2^3×4^2 equals 128
8 to the 6th is 262144 and to the 5th is 32768
Find an equation of the form f(x)=ax^2+bx+c. must solve algebraically and check using a calculator (state, the steps used to perform the check).
f(1)=4, f(2)=13, f(4)=46
The equation of the form [tex]f(x)=ax^2+bx+c[/tex] that must solve algebraically and f(1)=4, f(2)=13 and, f(4)=46 is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].
Putting x = 1 in the given equation, we get
[tex]f(1)=a(1)^2+b(1)+c[/tex]
f(1) = a + b + c = 4 ...(1)
Putting x = 2 in the given equation, we get
[tex]f(2)=a(2)^2+b(2)+c[/tex]
f(2) = 4a + 2b + c = 13 ...(2)
Putting x = 4 in the given equation, we get
[tex]f(4)=a(4)^2+b(4)+c[/tex]
f(4) = 16a + 4b + c = 46 ...(3)
Using elimination method to solve the set of linear equations, we get
(2) - (1), we get
3a + b = 9 ...(4)
(3) - (2), we get
12a + 2b = 33 ...(5)
Multiplying (4) by 2, we get
6a + 2b = 18 ...(6)
(5) - (6), we get
6a = 15
a = 15/6 = 5/2
Putting a = 5/2 in (4), we get
3(5/2) + b = 9
15/2 + b = 18/2
b = 3/2
Putting the values of a and b in (1), we get
5/2 + 3/2 + c = 9
4 + c = 9
c = 9 - 4
c = 5
Hence, the equation is [tex]\frac{5}{2}x^2+\frac{3}{2}x+5[/tex].
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Find the volume of the figure. Round to the nearest hundredth of a unit.
Check the picture below.
so is more or less the figure of a rectangular prism with a right-cylinder underneath that has a radius of 1, since it has a diameter of 2.
now, if we just get the volume of the prism, and then the volume of half of the cylinder, because only half-cylinder is really inside the prism, and then subtract that half-cylinder volume from that of the prism, what's leftover is the volume of the figure only.
[tex]\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}\hspace{5em}\stackrel{\textit{volume of half a cylinder}}{V=\cfrac{1}{2}\pi r^2 h} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE volumes}}{\stackrel{prism}{(4)(4)(8)}~~ - ~~\stackrel{half~cylinder}{\cfrac{1}{2}\pi (\underset{r}{1})^2(\underset{h}{8})}}\implies 128~~ - ~~4\pi ~~ \approx ~~\text{\LARGE 115.43}~cm^3[/tex]
An astronaut on the moon throws a baseball upward. The height of the ball in feet
(y) is related to the number of seconds since the ball was thrown (x).
y = -2.7x² + 30x + 6.5
How high will the ball be after 3 seconds? Use your calculator to pull up a function
table to help you. (6 points total)
The height of the ball be after 3 seconds will be 72.2 feet.
How to calculate the height?From the information given, it should be noted that the astronaut on the moon throws a baseball upward and the height of the ball in feet
(y) is related to the number of seconds since the ball was thrown (x).
In this case, it should be noted that the function is illustrated as:
y = -2.7x² + 30x + 6.5
Therefore, it was given that x = 3. It should be noted that this will be put back into the function. This will be:
y = -2.7x² + 30x + 6.5
y = -2.7(3)² + 30(3) + 6.5
y = -24.3 + 90 + 6.5
y = 72.2
The height is 72.2 feet.
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Write an equation of the line that passes through (-5,4) and is perpendicular to the line that is defined by x-2y=-4
By using the equation of the line and properties of perpendicular lines, we find that the equation of the line is equal to y = - 2 · x - 6.
How to determine the equation of a line
Herein we need to find a line that passes through point (- 5, 4) and is perpendicular to a given line in implicit form: x - 2 · y = - 4. The complete procedure is shown below. First, rewrite the equation of the perpendicular line into explicit form:
x - 2 · y = - 4
2 · y = x + 4
y = (1 / 2) · x + 2
Second, determine the slope of the new line:
m · m' = - 1
(1 / 2) · m' = - 1
m' = - 2
Third, calculate the intercept of the new line:
b = y - m · x
b = 4 - (- 2) · (- 5)
b = 4 - 10
b = - 6
Fourth, complete the new equation of the line:
y = - 2 · x - 6
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PLEASE HELP I GIVE BRAINLYS TO THE FIRST ONE THAT GETS IT RIGHT
Answer: 6 blue, 6 yellow, 6 red
Step-by-step explanation:
A fair stack of cards is an equal amount of cards.
3 colors, 18 total
18 / 3 = 6
Therefore 6 of each
AO. Use the appropriate divisibility rule to determine which of the following numbers is a factor of
315438530. (In each case, state "Yes" or "No" and explain briefly your use of the rule.)
(i) 2, (ii) 3, (iii) 4, (iv) 5, (v) 6, (vi) 8, (vii) 11
The results based on divisibility rules are given below -
What are divisibility rules?A divisibility rule is a convenient shorthand for checking if an integer is divisible by a given set divisor without actually doing the division, typically by looking at the digits of the number.
Rule of Divisibility for 2: The given integer's final/unit digit must be an even number or a multiple of two, i.e., 0, 2, 4, 6, and 8.
Dividend Rule for Number 5: The provided number should have a unit digit of 0 or 5.
Yes, As number on ones place is multiple of 2.No, as the sum of numbers is not divisible by 3.No, As numbers on tens place are not divisible by 4.Yes, As number on ones place is 0.No, As the number is divisible by 2 but not 3.No, As number on hundreds place is not divisible by 8.Yes, using even odd method.To learn more about divisibility rules from given link
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At a carnival, 5/8 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?
2.5% of 8 = .2
5/8 + .2/8 = 5.2/8
5.2/8 = .65 x 100 = 65%
65% of games cost 1 or 2 dollars
100% - 65% = 35%
!! after doing it i did realize I could've just converted 5/8 into a percent than added it.
or
5/8 = .625 + .025 = .65 x 100 = 65%; 100% - 65% = 35%
7 Describe the error in solving the equation
(1) 3 (X + 4) = 13
(2) 3x + 4 =13
(3) 3 x = 9
(14)X = 3
the error in the equation is 3 is not multiplied by 4 which gives wrong value of x .
What is the linear equation ?A linear equation is a first-order (linear) term and a constant in an algebraic equation of the type y=mx+b, where m is the slope and b is the y-intercept. The previous equation, which has the variables y and x, is sometimes referred to as a "linear equation with two variables."
The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. Finding both the intercepts of an equation in this way is quite easy (x and y).
Calculation3 (x + 4) = 13
3x + 12 = 13 \\the place where the error was occurred in the question\\
3x = 1
x = 1/3
this is correct value of x
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Evaluate for the given values
We are going to evaluate for the giving values
x | y | x + 3y
0 | 4 | 0 + 3(4) = 3(4) = 12
2 | 3 | 2 + 3(3) = 2 + 9 = 11
4 | 2 | 4 + 3(2) = 4 + 6 = 10
3 | 6 | 3 + 3(6) = 3 + 18 = 21
helppppp. can you help please?
P (-5), replace x by (-5).
[tex]p(x)=8(-5)^4+39(-5)^3-n(-5)^2+6(-5)-20[/tex]Solve the parentheses:
[tex]p(x)=8(625)+39(-125)-n(25)-30-20[/tex][tex]p(x)=5,000-4,875-25n-30-20[/tex]Combine like terms:
[tex]p(-5)=75-25n[/tex]A normal distribution has a mean of u = 60 and a standard deviation of o = 18. For each of the follow-
ing samples, compute the z-score for the sample mean
and determine whether the sample mean is a typical,
representative value or an extreme value for a sample
of this size.
a. M= 67 for n = 4 scores
b. M = 67 for n = = 36 scores
Answer:
HI
Step-by-step explanation:
HOW ARE
Please help I’ll mark you as brainliest if correct!!
Answer:
1 hour, 28 minutes, 15 seconds
Step-by-step explanation:
Given that AABC ADEF. Find the scale factor from AABC to ADEF.A2x24B20CDX-2E5
1) To find the scale factor for these triangles, we need to write a pair of ratios and then solve for x:
[tex]\begin{gathered} \frac{2x}{4}=\frac{20}{5} \\ \\ 10x=80 \\ \\ \frac{10x}{10}=\frac{80}{10} \\ \\ x=8 \\ \\ \end{gathered}[/tex]Now, we can plug x=8 into those:
[tex][/tex]