The rate of the passenger train is 100 miles per hour.
Given:
1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.
2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.
We can set up equations based on the distances traveled and the rates:
1. For the passenger train:
[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]
Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:
[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]
So, the rate of the passenger train is 100 miles per hour.
In 2012 there were approximately 8950 public librarys in the United States a survey found that 76% of the library's offered free access to the electronic books based on this information how many public library offered free access electronic books in 2012
Answer:
6,802
Step-by-step explanation:
Our first step is to change 76% into a decimal:
76% -> [tex]\frac{76}{100}[/tex] -> 0.76
Next, lets multiply and solve for x:
[tex]x=8,950(0.76)[/tex]
[tex]x = 6,802[/tex]
There were 6,802 public libraries that offered free access electronic books in 2012.
Answer:
6802 Libraries offered free electronic books.
Step-by-step explanation:
A company has been rating television programs for more than 60 years. It uses several sampling procedures, but its main one is to track the viewing patterns of 20,000 households. These contain more than 45,000 people and are chosen to form a cross-section of the overall population. The households represent various locations, ethnic groups, and income brackets. The data gathered from the sample of 20,000 households are used to draw inferences about the population of all households in the United States. Complete parts (a) and (b) below. What strata are used in the sample? Choose the correct answer below.
A. The various locations, ethnic groups, and income brackets that are represented
B. The various sampling procedures and viewing patterns
C. The number of households and people that are chosen
D. The television ratings
Why is it important to have a stratified sample for these ratings? Choose the correct answer below.
A. Stratified sampling ensures that all of the members of one or more groups are used.
B. Stratified sampling ensures that the television ratings are accurate.
C. Stratified sampling ensures that each segment of the population is represented.
D. Stratified sampling ensures that only households in the U.S. are sampled
Using stratified sampling concepts, it is found that the correct options are:
A. The various locations, ethnic groups, and income brackets that are representedC. Stratified sampling ensures that each segment of the population is represented.Stratified sampling divides the population into groups, called stratas, and a few elements of each group are surveyed.
In this problem, the households are divided to represents various locations, ethnic groups, and income brackets, hence, those are the stratas.
Stratified sampling is used because ensures that all segments of the population are represented.
You can learn more about stratified sampling at https://brainly.com/question/16252312
The sum of three consecutive numbers is one hundred thirty - eight.
What is the smallest of the three numbers
Answer:
45
Step-by-step explanation:
The average of the three numbers is the middle one: 138/3 = 46. Then the smallest of the three consecutive numbers is 45.
Final answer:
The smallest of the three consecutive numbers that add up to 138 is 45.
Explanation:
To find the smallest of the three consecutive numbers that add up to one hundred thirty-eight, we first need to represent the numbers algebraically.
Let x be the smallest number, x+1 is the next number, and x+2 is the largest number.
The equation that represents their sum is:
x + (x + 1) + (x + 2) = 138
To solve for x, we combine like terms:
3x + 3 = 138
Then we subtract 3 from both sides:
3x = 135
And divide both sides by 3 to find x:
x = 135 / 3
x = 45
Therefore, the smallest number is 45.
To write 11x2+17x−10 in factored form, Diego first listed pairs of factors of -10. (_+5)(_+-2) (_+2)(_+-5) (_+10)(_+-1) (_+1)(_+-10) Use what Diego started to complete the rewriting. Only one of the factored forms needs to be used and completed.
Answer:
The factored form of the polynomial is 11*(x+2)*(x-5/11). The root found was r = -2
Step-by-step explanation:
If you take a positive value of x, you will most likely obtain positive results, since 11x² + 17x ≥ 11 + 17 = 28 for x ≥1, which means that 11x²+17x-10 ≥ 28-10 = 18 > 0.
Therefore, we prove with negative values.
x = -1: 11*(-1)²+17*(-1) - 10 = -16x = -2: 11*(-2)² + 17*(-2) - 10 = 44-34-10 = 0Therefore, -2 is a root. We can find the other knowing that
p(x) = 11*(x-r₁)*(x-r₂) = 11*(x-(-2)) * (x-r₂) = 11*(x+2)*(x-r₂)
The independent term is 11*2*(-r₂) = -22r₂ = -10
thus, r₂ = -10/-22 = 5/11.
Therefore, p(x) = 11*(x+2)*(x-5/11)
To write 11x2+17x−10 in factored form we find two numbers whose sum is 17 and product is -110. The correct pair is 2 and -55 which leads to the factored form (11x - 55)(x + 2).
Explanation:The question involves factoring a quadratic expression, 11x2+17x−10. To re-write this expression in factored form, one needs to find two numbers, such that their sum equals to the coefficient of x, 17, and their product equals to the product of the coefficient of x² and the constant term (11*(-10)=-110). Diego started by listing all pairs of factors of the constant term, -10. The correct pair here, considering the product and the sum, are 2 and -55, because 2*(-55)=-110 and 2+(-55)=17. Therefore, our factored form will be: (11x - 55)(x + 2).
Learn more about Factoring Quadratic Expressions here:https://brainly.com/question/8342271
#SPJ11
ILL GIVE YOU BRAINLIEST!!PLEASEEE HELPPP MEEEE
Answer:I can't really tell what B says could you do another pic
Step-by-step explanation:
Answer:
Across the x axis.
Step-by-step explanation:
The radius of the water bottle is about _______cm.
Answer:
45.216
Step-by-step explanation:
2 x 3.14 x7.2
Answer:
Step-by-step explanation:
Volume of water bottle = 143 cubic cm
πr²h = 143
3.14*r²*7.2 = 143
[tex]r^{2}=\frac{143}{3.14*7.2}\\\\r^{2}=6.325\\[/tex]
r = 2.51
r = 2.5 cm
What percentage of the data values falls between the values of 3 and 24 in the data set shown?
A box-and-whisker plot. The number line goes from 0 to 25. The whiskers range from 3 to 24, and the box ranges from 6 to 19. A line divides the box at 15.
Answer
25 percent
Step-by-step explanation:
Answer:
The correct answer is 100%
Step-by-step explanation:
:>
Which is equivalent to log Subscript 2 Baseline n = 4?
A)log n = StartFraction log 2 Over 4 EndFraction
B)n = StartFraction log 2 Over log 4 EndFraction
C)n = log 4 times log 2
D)log n = 4 log 2
Answer:
D) log n = 4 log 2Step-by-step explanation:
Given
log₂ n = 4Compare the given with the options to identify equivalents
A)
log n = log 2 / 4 log₂ n / log₂ 10 = 1/ log₂ 10 ÷ 4log₂ n = 1/4Not equivalent
B)
n = log 2 / log 4n log 4 = log 2n log₂ 4 / log₂ 10 = 1 / log₂ 10n log₂ 4 = 1Not equivalent
C)
n = log 4 × log 2n = log₂ 4/ log₂ 10 × 1/ log₂ 10n = 2 /(log₂ 10)²n (log₂ 10)² = 2Not equivalent
D)
log n = 4 log 2log₂ n / log₂ 10 = 4 × 1/log₂ 10log₂ n = 4Equivalent
At the 2010 Winter Olympics in Vancouver, the top 8 countries got a total of 60 gold medals. Of the 60, Russia got 3 gold medals. Write and solve an equation to find what percent of the total gold medals, for the top countries, Russia got.
Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.
Let's denote the total number of gold medals obtained by Russia as [tex]\( x \)[/tex]. Since we know Russia got 3 gold medals, we have [tex]\( x = 3 \)[/tex].
Now, let's denote the total number of gold medals obtained by the top 8 countries (including Russia) as T. We're told that the total number of gold medals obtained by all top 8 countries combined is 60. Since Russia got 3 gold medals, the gold medals obtained by the other top 7 countries is [tex]\( T - 3 \)[/tex].
So, the percentage of gold medals obtained by Russia can be calculated as:
Percentage of gold medals obtained by Russia = [tex]\frac{\text{Number of gold medals obtained by Russia}}{\text{Total number of gold medals obtained by the top 8 countries}} \times 100\%\][/tex]
Substituting the known values:
[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{T} \times 100\%\][/tex]
We know that the total number of gold medals obtained by the top 8 countries is 60, so [tex]\( T = 60 \).[/tex] Substituting this into the equation:
[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{3}{60} \times 100\%\][/tex]
Solving this equation:
[tex]\[\text{Percentage of gold medals obtained by Russia} = \frac{1}{20} \times 100\% = 5\%\][/tex]
So, Russia obtained [tex]\( 5\% \)[/tex]of the total gold medals for the top 8 countries.
3n^2−2n−8 Factoring trinomials II
Answer:
(3n + 4) (n-2)
Step-by-step explanation:
Are you asking to factor this 3n^2 - 2n -8 ?
If so the best way to do this problem is with the X method.
top: 3*(-8)
left: factor of 3*-8 right: factor of 3*-8
bottom: -2
try the factors 4 and -6 because 4*-6 = 3 *-8 = -24
Because notice that 4 + -6 = -2
so:
3n^2 -2n - 8 can be rewritten as 3n^2 -6n + 4n - 8
We should first use Distributive property to factor: 3n^2 -6n + 4n - 8
3n^2 -6n + 4n - 8 = 3n (n - 2) + 4(n - 2)
Now we factor by grouping here : (3n + 4) (n-2)
I factored out the group (n-2)
Therefore: (3n + 4) (n-2) = 3n^2 -2n - 8
Two of the steps in the derivation of the quadratic
formula are shown below.
Which operation is performed in the derivation of the
quadratic formula moving from Step 6 to Step 7?
subtracting bi from both sides of the equation
Step 6: barangan = (x +
Step 7: tvb22400 = x +
squaring both sides of the equation
taking the square root of both sides of the equation
taking the square root of the discriminant
Please help quick
Answer:
a
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
taking the square root of both sides of the equation
can somebody do this
6x²-x-2=0
Answer:
X= 1 + 7/12
x = 1 - 7/12
Step-by-step explanation:
Answer:
[tex]x=\frac{19}{12}\\ or\\x=\frac{5}{12}[/tex]
Step-by-step explanation:
[tex]6x^2-x-2=0[/tex]
a=6
b=-1
c=-2
[tex]x=-b\frac{+}{}\frac{\sqrt[]{b^2-4ac} }{2a}[/tex]
[tex]x=-(-1)\frac{+}{}\frac{\sqrt[]{(-1)^2-4(6)(-2)} }{2(6)}[/tex]
[tex]x=1\frac{+}{}\frac{\sqrt[]{1+48} }{12}[/tex]
[tex]x=1\frac{+}{}\frac{\sqrt[]{49} }{12}[/tex]
[tex]x=1\frac{+}{}\frac{7}{12}[/tex]
------------------------------
[tex]x=1+\frac{7}{12}[/tex]
[tex]x=1-\frac{7}{12}[/tex]
------------------------------
[tex]1+\frac{7}{12}=\frac{(1*12)+(7*1)}{12} =\frac{12+7}{12} =\frac{19}{12}[/tex]
------------------------------
[tex]1-\frac{7}{12}=\frac{(1*12)-(7*1)}{12} =\frac{12-7}{12} =\frac{5}{12}[/tex]
Helena wants to paint a box in the shape of a cube with sides that are 18 inches long. what is the surface area that Helena will paint?
Answer:
1944 Inches Squared
Step-by-step explanation:
Surface area Formula for a Cube:
[tex]A = 6a^2[/tex]
The "edge", which is also the side, is 18 inches.
[tex]a = 18[/tex]
Solve the formula.
[tex]A= 6a^2 = 6(18)^2 = 6 * 18^2\\18^2 = 324\\324 * 6 = 1944\\A=1944[/tex]
The cube's surface area should be 1944 square inches.
Answer:
Step-by-step explanation:
1944 Inches Squared
Step-by-step explanation:
Surface area Formula for a Cube:
The "edge", which is also the side, is 18 inches.
Solve the formula.
The model of a new apartment building have dimensions of 10 inches in width, 18 inches in length and 28 inches in height. The architect plans for the building to be 144 times the dimensions of the model. What will be the volume and surface area or the new building when it is completed?
The volume of the new building is 11,726,069,760 cubic inches, and its surface area is 51,555,840 square inches.
To find the volume and surface area of the new building, we first need to calculate the dimensions of the new building by scaling up the dimensions of the model by a factor of 144.
1. Dimensions of the new building:
-[tex]Width: \(10 \times 144 = 1440\) inches[/tex]
- [tex]Length: \(18 \times 144 = 2592\) inches[/tex]
- [tex]Height: \(28 \times 144 = 4032\) inches[/tex]
2. Volume of the new building:
The volume of a rectangular prism (building) is calculated by multiplying its length, width, and height.
[tex]\[Volume = \text{Length} \times \text{Width} \times \text{Height}\][/tex]
Substituting the given dimensions:
[tex]\[Volume = 2592 \times 1440 \times 4032\][/tex]
[tex]\[Volume = 11,726,069,760 \text{ cubic inches}\][/tex]
3. Surface area of the new building:
The surface area of a rectangular prism (building) is calculated by adding the areas of all six sides.
[tex]\[Surface\,Area = 2(\text{Length} \times \text{Width} + \text{Length} \times \text{Height} + \text{Width} \times \text{Height})\][/tex]
Substituting the given dimensions:
[tex]\[Surface\,Area = 2(2592 \times 1440 + 2592 \times 4032 + 1440 \times 4032)\][/tex]
[tex]\[Surface\,Area = 51,555,840 \text{ square inches}\][/tex]
So, when the new building is completed:
- The volume will be [tex]\(11,726,069,760 \text{ cubic inches}\).[/tex]
- The surface area will be [tex]\(51,555,840 \text{ square inches}\).[/tex]
Can three segments with length 4 cm 6 cm and 11 cm be assembled to form an acute triangle a right triangle or an obtuse triangle?
Final answer:
Three segments with lengths 4 cm, 6 cm, and 11 cm cannot form a triangle because the sum of the lengths of the two shorter sides is not greater than the length of the longest side, violating the Triangle Inequality Theorem.
Explanation:
To determine whether three segments with lengths 4 cm, 6 cm, and 11 cm can form a triangle, we must consider the Triangle Inequality Theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. If we attempt to apply this to the given lengths:
4 cm + 6 cm > 11 cm (False)
4 cm + 11 cm > 6 cm (True)
6 cm + 11 cm > 4 cm (True)
Since the sum of the lengths of the two shorter sides (4 cm + 6 cm) is not greater than the length of the longest side (11 cm), these three segments cannot form a triangle, whether it is an acute triangle, right triangle, or obtuse triangle.
If they were able to form a triangle, to classify the type of triangle, we would use the Converse of the Pythagorean Theorem. This theorem helps us understand if a triangle is acute, right, or obtuse:
In a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.
If the square of the longest side is greater than the sum of the squares of the other two sides, the triangle is obtuse.
If the square of the longest side is less than the sum of the squares of the other two sides, the triangle is acute.
However, since a triangle cannot be formed with these segments, we do not need to apply these rules here
17 points! Which system of equations has an infinite number of solutions?
2x – 6y = 18
x – y = 9
2x – 6y = 18
x + 3y = 9
2x – 6y = 18
x – 3y = 9
Answer:
The bottom equation is infinite solutions ( please give branliest)
2x - 6y = 18
x - 3y = 9
Step-by-step explanation:
Using substitution,
x=3y + 9
6x - 6x + 18 = 18
0 = 18 - 18
0 = 0
Answer: Last one:)
Step-by-step explanation:
Just did it
Simplify the trigonometric function
Answer:
a. csc²θ
Step-by-step explanation:
You can use the identities ...
1 +tan² = sec²
cot = cos/sin
sec = 1/cos
csc = 1/sin
___
Then the expression becomes ...
[tex]\cot^2{\theta}(1+\tan^2{\theta})=\cot^2{\theta}\sec^2{\theta}=\dfrac{\cos^2{\theta}}{\sin^2{\theta}\cos^2{\theta}}=\dfrac{1}{\sin^2{\theta}}\\\\=\boxed{\csc^2{\theta}}[/tex]
Alice Jones worked 32 hours this week. She paid $4.00 per hour. She also earned $250 in tips. What is Alices gross pay for this week?
Answer:378
Step-by-step explanation:32 times 4=178 +250=378
Alice Jones's gross pay for the week is the sum of her hourly earnings ($128 from working 32 hours at $4.00 per hour) and her tips ($250), totalling $378.
To calculate Alice Jones's gross pay, we need to consider both her hourly wage and her tips. Alice worked 32 hours this week and was paid $4.00 per hour. This means her earnings from her hourly wage are:
32 hours times $4.00/hour = $128
Alice also earned $250 in tips. To find her gross pay for the week, we add her hourly earnings to her tips:
$128 + $250 = $378
Therefore, Alice's gross pay for the week is $378.
A rectangular prism is 10.8 yards long and 10.1 yards wide. Its volume is 218.16 cubic yards. What is the height of the rectangular prism?
Answer:
2 yards
Step-by-step explanation:
[tex]\frac{218.16}{10.8\cdot 10.1}=2[/tex] yards. Hope this helps!
Answer:
get the brainliest duck
Step-by-step explanation:
The top two nets represent the triangular prisms that are attached to the bases of a rectangular prism. The composite figure is composed of all three prisms. The shaded areas are faces that are shared between the prisms. What is the total surface area of the composite figure?
78 square units
144 square units
282 square units
342 square units
Answer:
cx
Step-by-step explanation:
Answer:
the answer is C 282
Step-by-step explanation:
Five thousand, three hundred twenty people are on a cruise. If each dinner table seats 10 people, how many dinner tables does the cruise line need to provide?
tables
Answer:
532
Step-by-step explanation:
divide 5,320 by 10
A cooler contains five bottles of lemonade four bottles of water and three bottles of juice. Each is likely to be chosen. Describe a model that can be used to simulate the situation
Answer:Since each type of drink (lemonade, water, and juice) is equally likely to be chosen, the probability of choosing a type of drink is 1 in 3 picks. Thus, in order to get all three types of drinks, one must pick 3
Step-by-step explanation:
What is 145 divided by 788
Answer:
0.18401015
Step-by-step explanation:
You should use an online calculator
Sally has $21.40 in dimes and quarters. There are 100 coins in all. How many of each coin does she have?
x = dimes
y = quarters
We also know:
Dimes: 0.10
Quarters: 0.25
100 = x + y
So, 0.10x + 0.25y = 100
And, y = 100 - x
Let’s use substitution:
0.10x + 0.25( 100 - x ) = 100
= 0.10x + 25 - 0.25x = 100
= 25 - 100 = 0.25x - 0.10x
= (-75) = 0.15x
x = (-75) divide by 0.15
x = (-500)
In Euclidean geometry, the sum of the lengths of 2 sides of a triangle is greater than the length of the third side. The lengths of 3 sides of a triangle are 3x, 7, and 12.
Answer:[tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]
Step-by-step explanation:
Given
length of three sides are
[tex]3x, 7\ and\ 12[/tex]
according to Euclidean geometry
[tex]7+12>3x[/tex]
[tex]19>3x[/tex]
[tex]\frac{19}{3}>x[/tex]
also
[tex]3x+7>12[/tex]
[tex]3x>5[/tex]
[tex]x>\frac{5}{3}[/tex]
therefore value of [tex]x \in (\frac{5}{3},\frac{19}{3})[/tex]
If x is an integer then x can be [tex]2,3,4,5,6[/tex]
A cable running from the top of a utility pole to the ground exerts a horizontal pull of
800 Newtons and a vertical pull of 800V3 Newtons. What is the sine of the angle o
between the cable and the ground? What is the measure of this angle?
Answer:
a. (√3)/2
b. 60 degrees.
Step-by-step explanation:
Please kindly check the attached files for explanation.
The sine of the angle is √3 / 2, and the measure of the angle is 60°.
Finding the Angle Between a Cable and the Ground
To determine the sine of the angle ( heta) between the cable and the ground, we need to use the horizontal and vertical forces exerted by the cable. We have a horizontal pull of 800 Newtons and a vertical pull of 800√3 Newtons.
First, we calculate the sine of the angle using the formula:
Sine ( heta) = Opposite / Hypotenuse
Here,
Opposite = Vertical Pull = 800√3 N
Hypotenuse = Resultant Force = √[(Horizontal Pull)^2 + (Vertical Pull)^2] = √[(800)^2 + (800√3)^2] = 1600 N
Thus,
Sine ( heta) = 800√3 / 1600 = √3 / 2
We know that the angle heta with a sine value of √3 / 2 is 60 degrees (or heta = 60°).
In conclusion, sine of the angle is √3 / 2, and the measure of the angle is 60°.
Are the two cylinders similar? The diagrams are not drawn to scale.
a) no
b) yes
c) impossible to tell
for search: 8.32 10.192 2.6 3.64
thank you!
Answer:
a) no
Step-by-step explanation:
-The diagrams can be said to be mathematically similar if the dimensions of their corresponding sides enlarge or reduce by the same factor.
-We therefore determine the enlargement factor for both the radius and height as below:
-Let k be the scale factor
[tex]k_r=\frac{R}{r}\\\\=\frac{3.64}{2.6}\\\\=1.4\\\\k_h=\frac{H}{h}\\\\=\frac{10.192}{8.32}\\\\=1.225\\\\k_r\neq k_h[/tex]
Hence, the cylinders are not mathematically similar since the enlargment factors for the radius and height are not equal.
Answer:
Surface Area and Volume Unit Test
1. 14
2. hexagon
3. 224 m2
4. 896 pi in.2
5. 405 in.2
6. 49,009 m2
7. 4,910.4 yd3
8. 3.6 in
9. 4,608 cm3
10. 1,296 cm3
11. 1,442.0 yd3
12. 2,158 m2
13. no
14. 7 : 10
15. 100 m2
16. one-point perspective
17. 18.3 cm
suppose ACT Mathematics scores are normally distributed with a mean of 21.3 and a standard deviation of 5.3. A university plans to send letters of recognition to students whose scores are in the top 11%. What is the minimum score required for a letter of recognition
Answer: the minimum score required for a letter of recognition is 27.8
Step-by-step explanation:
Suppose ACT Mathematics scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = ACT Mathematics scores.
µ = mean score
σ = standard deviation
From the information given,
µ = 21.3
σ = 5.3
The probability of students whose scores are in the top 11 % would be be (1 - 11/100) = (1 - 0.11) = 0.89
Looking at the normal distribution table, the z score corresponding to the probability value is .23
Therefore,
1.23 = (x - 21.3)/5.3
Cross multiplying by 8.6, it becomes
1.23 × 5.3 = x - 21.3
6.519 = x - 21.3
x = 6.519 + 21.3
x = 27.8 to the nearest whole number
Final answer:
The minimum ACT Mathematics score required to be in the top 11% with a mean of 21.3 and a standard deviation of 5.3 is approximately 27.85, which is usually rounded to 28.
Explanation:
Top 11% for ACT Mathematics Score Requirement
If ACT Mathematics scores are normally distributed with a mean of 21.3 and a standard deviation of 5.3, the score corresponding to the top 11% can be found by determining the z-score that corresponds to the 89th percentile (100% - 11% = 89%). To find this z-score, one would typically use a z-score table or a statistical software. Once the z-score for the 89th percentile is found, it can be converted to an ACT score using the formula:
Z = (X - μ) / σ
where Z is the z-score, X is the ACT score, μ (mu) is the mean, and σ (sigma) is the standard deviation. Solving for X:
X = Z×σ + μ
Assuming the z-score for the 89th percentile is approximately 1.23, the minimum required score for a letter of recognition would be:
X = 1.23×5.3 + 21.3
X ≈ 1.23×5.3 + 21.3
X ≈ 6.549 + 21.3
X ≈ 27.849
Therefore, the minimum score required for a letter of recognition would be approximately 27.85, which can be rounded as appropriate for the context (usually to the nearest whole number, giving a score of 28).
14x – 2y = 1
2x - Y= -2
Joan has saved 7 quarters from washing cars how many cents does Joan have?
Answer:
175 cents
Step-by-step explanation:
1 quarter is equal to 25 cents.
Since there are 7 of them,
7 times 25 cents = 175 cents