A quadrilateral has two angles that measure 100° and 90°. The other two angles are in a ratio of 7:10. What are the measures of those two angles?

A test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.

To find the test score that is 1.4 standard deviations above the mean, we need to use the formula:

z = (x - μ) / σ

where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.

In this case, we know that z = 1.4, μ = 100, and σ = 5. So we can rearrange the formula to solve for x:

x = z * σ + μ

Substituting the values we know, we get:

x = 1.4 * 5 + 100 = 107

Therefore, a test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.

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Answer:

  A.  Bimodal

Step-by-step explanation:

You want a description of the shape of the histogram shown.

The mode of a dataset is the value that appears most often. When two values have that distinction, the data is said to be "bimodal."

Here, the most a data item appears is 6 times. Two data items have that distinction: 2 and 7. Hence, the shape of the distribution is ...

  A.  Bimodal

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A sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units.

To find the sample size needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, we can use the formula:

n = [ (z * σ) / E ]^2

where n is the required sample size, z is the critical value for the desired confidence level (95% confidence level corresponds to a z-value of 1.96), σ is the population standard deviation (given as the square root of the variance, which is √(70) ≈ 8.37), and E is the maximum error, or the maximum difference between the sample mean and population mean that we are willing to tolerate (which is given as 2.5 units).

Substituting the given values into the formula, we get:

n = [ (1.96 * 8.37) / 2.5 ]^2

n ≈ 43.48

Rounding up to the nearest whole number, we get a required sample size of n = 44.

Therefore, a sample size of 44 is needed to assure with 95% confidence that the sample mean will not differ from the population mean by more than 2.5 units, assuming a normal distribution with a population variance of 70.

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scores on a certain test are normally distributed with a variance of 70 . a researcher wishes to estimate the mean score achieved by all adults on the test. find the sample size needed to assure with 95 percent confidence that the sample mean will not differ from the population mean by more than 2.5 units.

Since the research company is making a claim about the proportion of college students who shop online and Jamila is taking a sample of college students to test this claim, she should use a one-proportion z-test.

A one-proportion z-test is used to test whether the proportion of successes in a sample is significantly different from a hypothesized proportion. Here, the hypothesized proportion is 75% (the claim made by the research company) and the sample proportion is 120/200 = 0.6.

Jamila can use the one-proportion z-test to determine whether the difference between the sample proportion and the hypothesized proportion is statistically significant. The null hypothesis is that the sample proportion is equal to the hypothesized proportion (i.e., p = 0.75), and the alternative hypothesis is that the sample proportion is not equal to the hypothesized proportion (i.e., p ≠ 0.75).

Based on the sample size and the fact that the population standard deviation is not known, Jamila should use the normal approximation to the binomial distribution to perform the one-proportion z-test.

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Answer:

csc(t) = -3/2

Step-by-step explanation:

Given sin(-t) = 2/3, we can find the value of csc(t) as follows:

sin(-t) = 2/3

sin(t) = -2/3 (since the sine function is an odd function)

Since csc(t) = 1/sin(t), we have:

csc(t) = 1/sin(t) = 1/(-2/3) = -3/2

Answer:

[tex]\displaystyle \csc(t)=-\frac{3}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \sin(-t)=\frac{2}{3}\\\\\sin(t)=-\frac{2}{3}\\ \\\frac{1}{\sin(t)}=\frac{1}{-\frac{2}{3}}\\\\\\\csc(t)=-\frac{3}{2}[/tex]

The second step can be done because sin(-t) is an odd function.

Answer:x=251

Step-by-step explanation:

Step 1: Subtract 8 from both sides of the equation.

Explanation: Subtracting 8 from both sides of the equation keeps the equality balanced.

Step 2: x = 251

Explanation: Subtracting 8 from both sides of the equation gives us

x = 259 - 8 = 251.

Answer:

Step-by-step explanation:

x = -251

The number of Canadian dollars the bank exchange for $160 US dollars is 100.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.

A current medium of exchange in the form of coins and banknotes.

Given that, the bank would exchange 1.6 Canadian dollars for one US dollar.

Here, there are $160 US dollars.

So, number of Canadian dollars

= 160/1.6

= 100

Therefore, the number of Canadian dollars the bank exchange for $160 US dollars is 100.

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Part A: The  inequality to find the possible number of students, n, who ate the school lunch n > 542 students

Part B: The number of students, that possibly eat lunch at school is 542 or more students

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Part A; The number of students who bring lunch, B > 485 students

The number of students who eat lunch in school, E = B + 57

∴ E > 485 + 57

The number of students who can possibly eat lunch in school;

E > 542 students

Part B;

The number of students, n, that possibly eat lunch at school, are;

n = 542 or more students.

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The width of the bedroom is approximately 7.32 feet.

A rectangle is a four-sided figure with opposite sides being equal and parallel. The area of a rectangle is given by multiplying the length and width of the rectangle.

Let's assume that the width of the bedroom is 'x' feet. We know that the length of the room is 5 feet longer than its width. Therefore, the length of the room will be (x+5) feet.

Now, we can use the given area of the bedroom to set up an equation:

Area of rectangle = Length x Width

84 = (x+5) x x

Simplifying this equation, we get:

84 = x² + 5x

Rearranging, we get:

x² + 5x - 84 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± √(b² - 4ac))/2a

In this case, a = 1, b = 5 and c = -84. Substituting these values in the formula, we get:

x = (-5 ± √(5² - 4(1)(-84)))/2(1)

Simplifying this, we get:

x = (-5 ± √721)/2

We can ignore the negative root since the width of the bedroom cannot be negative. Therefore, the width of the bedroom is:

x = (-5 + √721)/2

x ≈ 7.32 feet

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The measure of each angle in complementary angles with measures 3x and 6x - 18 degrees is 36° and 54°.

We are given two angles 3x and 6x - 18 and these angles are complementary angles.

Complementary angles are those whose combined angle is 90 degrees or less. In other terms, two angles are said to be complimentary if they combine to make a right angle.

So, sum of 3x and 6x - 18 is 90°

     3x + 6x - 18 = 90°

                    9x = 108°

                      x = 12°

So, 3x = 3 × 12 = 36°

     6x - 18 = 6 × 12- 18 = 54°

Hence, the measure of each angle is 36° and 54°.

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Step-by-step explanation:

the zeros are the x-intercepts. because these are x values, when y (= f(x)) = 0.

a quadratic equation has 2 zeros (even if they are equal or complex numbers).

a quadratic equation

ax² + bx + c = 0

can always be solved by

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (-14 ± sqrt(14² - 4×2×20))/(2×2) =

= (-14 ± sqrt(196 - 160))/4 =

= (-14 ± sqrt(36))/4 = (-14 ± 6)/4

x1 = (-14 + 6)/4 = -8/4 = -2

x2 = (-14 - 6)/4 = -20/4 = -5

these are the 2 zeros (x-intercepts).

if you need the explicit points :

(-5, 0) and (-2, 0)

the y-intercept is the y-value when x = 0

y = 2×0² + 14×0 + 20 = 20

the explicit point : (0, 20)

Answer:

Step-by-step explanation:

Add all the number of goals and then divide by 10.

The number that, when raised to the power of three, equals 500000 is approximately 100.

To find this number, we can use the cube root function:

x^3 = 500000

x = cube root of (500000)

x = approximately 100

So, the number that, when raised to the power of three, equals 500000 is approximately 100.

Answer:

< 1 is acute (less than 90⁰)

<2 is acute

<BOA is obtuse (greater than 90⁰)

The area of the lawn in the scale drawing is approximately 996 square feet.

1. Measure the length and width of the lawn in inches on the scale drawing.

Length = 16.5 inches

Width = 15.5 inches

2. Convert the measurements to feet by dividing the inches by 12.

Length = 16.5/12 = 1.375 feet

Width = 15.5/12 = 1.291 feet

3. Calculate the area of the lawn by multiplying the length and width.

Area = 1.375 x 1.291 = 1.75 square feet

4. Multiply the area by the scale factor (in this case, 560) to get the actual area.

Area = 1.75 x 560 = 996 square feet

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Answer:it guarantees that people can all read and solve a problem in the same way.

Step-by-step explanation:

The expressions, in terms of t, for each vehicle so that the vehicles start separated and meet at 10 seconds is:

Tractor's position = Vt * t

Scooter's position = Vs * t

Let's assume that the starting point for both the tractor and the scooter is at "0". We can then write the expressions for their positions in terms of time "t" as follows:

For the tractor:

Tractor's speed = Vt

Tractor's position = Vt * t

For the scooter:

Scooter's speed = Vs

Scooter's position = Vs * t

Now, as both the vehicles meet at 10 seconds, we can write the equation:

Vt * 10 = Vs * 10

The above equation represents the position of both the vehicles at 10 seconds. If we assume the speed of the tractor and the scooter to be constant, then the equation gives us the relationship between their speeds.

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Answer:

x = 62

Step-by-step explanation:

2x ÷ 2 = 124 ÷ 2

x = 124 ÷ 2 = 62

Amount of iced-tea consumed during party was 92 cups, which is equivalent to 23 quarts. It's important to note difference between volume units such as cups and quarts, and the conversion factor between them.

To determine the number of cups of iced-tea that were consumed during the party, we need to subtract the amount that remained from the total amount that was in the drink dispenser at the start of the party.

One cup of iced tea is equal to 1/16 of a quart, so 7 cups is equal to

7 * (1/16) = 7/16 quarts.

Thus, the total amount of iced tea that was consumed during the party is 912 quarts -

7/16 quarts = 912 - 7/16

= 912 - 7 * (1/16)

= (912 * 16 - 7 * 1) / 16

= 1476 / 16

= 92.25 cups, rounded down to the nearest whole number, which is 92 cups.

It is important to note that the answer is given in cups and not quarts. Quarts is a unit of volume and cups is a unit of volume as well, but they are not equivalent. 1 quart is equal to 4 cups. If we wanted to express the amount of iced tea consumed in quarts, we would multiply the answer by 1/4.

In conclusion, the number of cups of iced tea consumed during the party is 92 cups, and if we express this in quarts it is equivalent to

92 * (1/4) = 23 quarts.

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Answer: 1/9 is the fraction form

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

[tex]3^{-2}[/tex]

= 1/[tex]3^{2}[/tex]

= 1/9

Answer:

The maximum of a set is the largest of a set.
arrange the terms in ascending order, 1.5, 3, 27.
take the biggest element of the ascending data set, which Is 27.

Step-by-step explanation

I tried my best I’m not the best at math. But I felt like someone needed help. I really hope you do well my friend. I’m sorry If the answer is in correct, I’m in geometry.

An equivalent expression for 18c+144 is 18(c+8), by factoring out the greatest common factor of the terms 18 and 144.

In the original expression 18c + 144, we have two terms that do not have any common factors other than 1. However, we can see that both terms are multiples of 18, with 18 as the greatest common factor. So, we can factor out the 18 to simplify the expression.

To factor out 18, we divide each term by 18, which gives us:

18c/18 + 144/18

The first term simplifies to c, and the second term simplifies to 8, so we have:

c + 8

This expression represents the sum of c and 8, and it is equivalent to 18c + 144. However, we can still simplify this expression further by factoring out the common factor of c + 8, which gives us:

c + 8 = 18(c + 8)

So, we have the equivalent expression 18(c + 8), which is the original expression 18c + 144 after factoring out the greatest common factor of 18.

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In a case whereby Jonah has $7,586 in an account that earns 10% interest compounded annually, the amount he will have in 3 years is $10,096.97

The concept that will be used here is counpound interest.

The  amount that will be present in the  account in 3 years can be estimated using the expression beleow which is:

FV = P(1 + r)^n

P represent the  amount in the account which is  $7,586

r  represen the interest rate which is 10/100 =0.01

n represent the number of years

FV  represent the future value

We can input all these values as :

FV =[ 7,586(1 + 0.1)^3]

= (7,586 x 1.1^3 )

= $10,096.97

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complete question:

Jonah has $7,586 in an account that earns 10% interest compounded annually.

To the nearest cent, how much will he have in 3 years?

The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

Examples of algebraic expressions include "3x + 4y", "2a^2 - 5b", and "(x + 3)(x - 2)".

Given expression ,

24a+(-26b)-13a+12b

= 24a - 13a +12 b - 26b

= 11a - 14b

Therefore, The expression 24a+(-26b)-13a+12b is equivalent to 11a-14b.

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Answer:

369 cans

Step-by-step explanation:

Add the two numbers of cans collected by each:

Alan:   154 cans

Betty:  215 cans

Total:  369 cans

The value of x for the trapezoid quadrilateral is equal to 5.

The quadrilateral is an isosceles trapezoid, with a line parallel to both opposing lines splitting the other two unparallelly going lines into equal halves. Hence, according to normal relations, the mid length is 5x-1.

The lengths of the opposing sides are 21 and 27 respectively. As a result, we may write 2(5x - 1) = 21 + 27.

Growing further, 10x - 2 = 48

10x = 48 + 2

10x = 50

Divide all sides by ten.

x = 50/10

x = 5

As a result, the value of x is 5.

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Answer: $35.

Step-by-step explanation: Let A = 2 movers and one truck for hour = $65

B = 3 movers and one truck for hour = $80

So, 1 mover = B - A

                  = $80 - $65

                  = $15

Hence, 2 movers cost = 2 × $15

                                  = $30

SO, rent of the truck hourly = A - cost of 2 movers

                                          = $65 - $30

                                          = $35

Therefore cost of renting the truck for an hour = $35

Answer:12

Step-by-step explanation:

8 times 3 equals 24.24 subtract36 get 12

Answer:

Step-by-step explanation:

2, there are 4, making it the most.

Answer:

2

Step-by-step explanation: this is because the plus sign splits the terms so simply 2 terms