10. In this university, among all students, 15% are senior, 25% are junior, 25% are sophomore, and so 35% are freshmen. Among senior, 40% have scholarship; among junior, 30% have scholarship; among sophomore, 20% have scholarship, and among freshmen, 10% have scholarship. Among those have scholoarship, what is the percentage of studens who are senior

Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

The volume of the figure, by splitting it into two cuboids comes to be 3300 ft³.

The volume of a cuboid is the product of its three dimensions i.e. length, breadth, and height.

Let us split the given figure into two cuboids

So, the volume of the figure will be the sum of the volume of both the cuboids.

So, the volume of the cuboid with dimensions 20 ft x 25 ft x 5ft

= 20 x 25 x 5

=2500 ft³.

The volume of the cuboid with dimensions  4 ft x 25ft x 8ft

=4 x 25x 8

=800 ft³.

So, the volume of the figure = 2500 + 800 =3300 ft³.

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Answer (let x be the number):

5x - 40 = x + 8

I hope this helps!

The number in the equation 5n - 40 + 8 = n is 8.

A numerical expression is formed by numbers and their operation.A numerical expression can also be constructed from given statements.

We can also construct numerical expression form real life scenarios.

According to to the question statement 40 subtracted from five times a number is 8 more than the number and we have to form an numerical expression.

Let the number be 'n'.

∴ 5n - 40 + 8 = n

5n - n = 40 - 8.

4n = 32.

n = 32/4.

n = 8.

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Let's check the rule

So

Let that ? be x

Answer:

x = 2.4

Step-by-step explanation:

4x + 5 / x + 7
combine like terms

X + 4x = 5x

5 + 7= 12

12/ 5x

Divide

12 /5= 2.4

X= 2.4

The cups of giardia-laced lemonade that Wiyot will have sold by the time his parents get a call from county health officials on day 8 is 75 cups.

From the information, Wiyot sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up.

This is an arithmetic sequence and will be expressed as:

= a + (n - 1)d

a = first term = 33

d = common difference = 6

n = 8

This will be:

= a + (n - 1)d

= 33 + (8 - 1)6

= 33 + (7 × 6)

= 33 + 42

= 75

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Answer:

Each interior angle = 180° -60° = 120°

Step-by-step explanation: We know that the three angles in a triangle, add up to 180°, and all the three angles are 60° in an equilateral triangle. The total number of angles of an enclosed space is 180° (n-2) where in is the number of sides.
A hexagon has six sides, so: s= 180° (6-2)

s= 180° x 4

s= 720°

now since in a regular shape, each interior angle is equal. We just divide the total interior angle with a number of sides

6.

720° divided by 6 is equal to 120°

Answer:

Her speed was 51.2 and the work i did was 460.8 / 9

Step-by-step explanation:

Answer:

za/2: Divide the confidence level by two, and look that area up in the z-table: .95 / 2 = 0.475. ...

E (margin of error): Divide the given width by 2. 6% / 2. ...

: use the given percentage. 41% = 0.41. ...

: subtract. from 1.

10 divided by 0 problem would NOT have a solution.

Given:

a. 10 divided by 2

b. 10 divided by 5

c. 10 divided by 0

d. 0 divided by 10

We know that ,

Integer divided by an integer is an integer

Therefore (a) and (b) will have a proper solution

We also know that ,

Zero divided by anything is Zero

Therefore (d) also have a unique answer that is zero

Now , We know that

Any numeric value divided by Zero tends to infinity .

Hence, 10 divided by 0 problem would NOT have a solution.

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Answer:

number 15 would be B sorry i dont understand number 14

Answer:

addition or subtraction (1.)

Step-by-step explanation:

Answer:

Divide both sides by a constant to simplify the equation.  Thus the second option.

Step-by-step explanation:

Solve for x:

9 - 10 x = -1

Hint: | Isolate terms with x to the left hand side.

Subtract 9 from both sides:

(9 - 9) - 10 x = -9 - 1

Hint: | Look for the difference of two identical terms.

9 - 9 = 0:

-10 x = -9 - 1

Hint: | Evaluate -9 - 1.

-9 - 1 = -10:

-10 x = -10

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -10 x = -10 by -10:

(-10 x)/(-10) = (-10)/(-10)

Hint: | Any nonzero number divided by itself is one.

(-10)/(-10) = 1:

x = (-10)/(-10)

Hint: | Any nonzero number divided by itself is one.

(-10)/(-10) = 1:

Answer:  x = 1

Answer:

14. 13.65

15. 7.53

17. 0.0371

18. 0.81

19. 0.864

Here are some answers! Hope this helps

The Function is increasing (-∞, 0), decreasing (2, ∞), and constant [0, 2].

The intervals on which the function is increasing, decreasing, or constant, we need to analyze the behavior of the function in each interval.

1. Interval t < 0:

In this interval, the function is given by f(t) = t + 2. Since the coefficient of t is positive (1), the function is increasing. Therefore, the interval t < 0 is an interval of increasing values.

2. Interval 0 ≤ t ≤ 2:

In this interval, the function is constant and given by f(t) = 2. The value of the function remains constant at 2 for all values of t in this interval.

3. Interval t > 2:

In this interval, the function is given by f(t) = -t + 4. Since the coefficient of t is negative (-1), the function is decreasing. Therefore, the interval t > 2 is an interval of decreasing values.

To summarize:

Increasing interval: t < 0

Decreasing interval: t > 2

Constant interval: 0 ≤ t ≤ 2

Using interval notation, we can express the intervals as follows:

Increasing interval: (-∞, 0)

Decreasing interval: (2, ∞)

Constant interval: [0, 2]

In interval notation, (a, b) denotes an open interval, which means it includes all values between a and b, but excludes the endpoints. [c, d] denotes a closed interval, which includes both endpoints c and d.

Therefore, the function is increasing on the interval (-∞, 0), decreasing on the interval (2, ∞), and constant on the interval [0, 2].

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Answer:

The integers are, -4, -3, -2, -1, 0, 1, 2, 3, 4, ... -- all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). For example, -5 is an integer but not a whole number or a natural number. An odd number is an integer when divided by two, either leaves a remainder or the result is a fraction. One is the first odd positive number but it does not leave a remainder 1. Some examples of odd numbers are 1, 3, 5, 7, 9, and 11. ... Since odd numbers are integers, negative numbers can be odd.

Answer:

1.) The point (24,30) would not be on the line

2.) The point (12,13) would not be on the line either

4.) The slope is a fraction of 2/1

Bonus: y = (2/1)x - 2

Step-by-step explanation:

For question three, I looked at the (6,10) point on the graph and compared it with the (a,8) point. That showed me that the y coordinate always moves by 2. Then I looked at the (6,10) coordinate and the (a,8) coordinate and the (4,b) coordinate and saw that there was one x coordinate between 6 and 4 so it must be five. That means the x coordinate moves by 1.

Let me know if you need more help!

:)

Complete question :

A college football coach wants to know if the is a correlation between his players' leg strength and the time it takes for them to sprint 40 yards. he sets up the following test and records the data:

Every day for a week, he counts how many times each player can leg press 350 pounds. The following week, he has each player sprint 40 yards every day. The tables shows the average number of leg-press repetitions and the average 40-yard dash time (in seconds) for seven randomly selected players. What is the equation of the line of best fit? How many seconds should he expect a player to take to run 40 yards if that player can do 22 leg-press repetitions?

Leg Press (reps)|40-yard Dash (s)

15 |5.2

18 |6.3

8 |6.8

30 |8.2

26 |8.0

12 |5.3

21 |5.9

Answer:

ŷ = 0.1073X + 4.5365

6.9

Step-by-step explanation:

Leg Press (reps)X:

15

18

8

30

26

12

21

Y:

5.2

6.3

6.8

8.2

8.0

5.3

5.9

Using a regression calculator :

The equation of line of best fit is :

ŷ = 0.1073X + 4.5365

Slope or gradient = 0.1073

Intercept = 4.5365

X = independent or predictor variable (leg press)

Y = predicted variable (40 yard dash)

B)

X = 22

Y = 0.1073(22) + 4.5365

Y = 6.8971

Y = 6.9

The expression of total amount paid in the first 12 months for the big screen TV is C. \(\frac{62*(1 - 1.04^{12})}{(1-1.04)}\)

To find the expression of the total amount paid in the first 12 months, we can use the formula for the sum of a geometric series which states: S = a(1-r^n) / (1-r)

Data:

First term (a) is $62

Common ratio (r) is 1.04

We have 12 terms (n) in the series.

Substituting the values, we get:

\(S = 62*(1 - 1.04^{12}) / (1-1.04)\\S = 62 * 15.0258054642\\S = 931.59993878\\S = $931.60\)

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Answer:

The answer is "A" i think not 100% sure

tell me if wrong

Answer:

cos θ = 4/5

Explanation given below in the image,

I hope my answer helps you.

\(nC0 + nC1 + ... + nCr + ... + nCn = 2^n\) is proved using the binomial theorem.

The binomial theorem states that:

\((x + y)^n = nC0 x^n y^0 + nC1 x^(n-1) y^1 + ... + nCr x^(n-r) y^r + ... + nCn x^0 y^n\)

where \(^nC_r\) represents the binomial coefficient.

We have,

We can prove that,

The sum of the binomial coefficients for \(^nC_0\) through \(^nC_n\) is equal to \(2^n\) using the binomial theorem.

From the theorem,

\((x + y)^n = nC0 x^n y^0 + nC1 x^(n-1) y^1 + ... + nCr x^(n-r) y^r + ... + nCn x^0 y^n\)

If we substitute x = y = 1 into this formula,

We get,

\((1 + 1)^n = nC0 1^n 1^0 + nC1 1^(n-1) 1^1 + ... + nCr 1^(n-r) 1^r + ... + nCn 1^0 1^n\)

Simplifying,

\(2^n = nC0 + nC1 + ... + nCr + ... + nCn\)

Since the sum of all binomial coefficients in the expansion  \((x + y)^n\) is equal to \(2^n\),

we have proven that,

\(nC0 + nC1 + ... + nCr + ... + nCn = 2^n\)

This proves the theorem.

Thus,

The sum of the binomial coefficients for \(^nC_0\) through \(^nC_n\) is equal to \(2^n\) is proved using the binomial theorem.

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Answer: I believe the answer is Goal-seeking i hope this helps

Step-by-step explanation:

Yes, the deviance statistic is often used to assess the fit of a statistical model for a binary response variable. In particular, the deviance statistic is a measure of the difference between the observed data and the fitted values predicted by the model. It can be used to test the goodness of fit of the model or to compare the fit of different models.

The deviance statistic has an asymptotic chi-squared distribution when the sample size is large and the model holds. This means that if the sample size is very large, the deviance statistic will approximately follow a chi-squared distribution with a certain number of degrees of freedom. The degrees of freedom are determined by the number of parameters in the model.

The deviance statistic can be used to perform a goodness of fit test by comparing the observed deviance to the expected deviance under the null hypothesis that the model fits the data well. If the observed deviance is significantly larger than the expected deviance, this suggests that the model does not fit the data well, and the null hypothesis should be rejected. On the other hand, if the observed deviance is not significantly different from the expected deviance, this suggests that the model fits the data well, and the null hypothesis should be accepted.

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The slope of the line tangent to the graph of h(x) = 1/x + 3 at the point when x is -6 is -1/36.

To determine the slope of the line tangent to the graph of the given function when x = -6;

Using alternative form of the definition of derivative.

f'(a) = lim (h->0) [f(a+h) - f(a)] / h

Using this formula for the given function;

h'(a) = lim (h->0) [h(a+h) - h(a)] / h

Now, substitute a = -6 into the formula:

h'(-6) = lim (h->0) [h(-6+h) - h(-6)] / h

Next, simplify the expression by plugging in the values:

h'(-6) = lim (h->0) [1/(-6+h) + 3 - (1/-6 + 3)] / h

Simplifying further:

h'(-6) = lim (h->0) [1/(-6+h) - 1/-6] / h

Now, let's combine the fractions with a common denominator:

h'(-6) = lim (h->0) [(-6 - (-6+h))/((-6+h)(-6))] / h

Simplifying the numerator:

h'(-6) = lim (h->0) [-h / ((-6+h)(-6))] / h

Canceling out the h's:

h'(-6) = lim (h->0) [-1 / ((-6+h)(-6))]

Taking the limit as h approaches 0:

h'(-6) = -1 / ((-6)(-6))

Simplifying further:

h'(-6) = -1 / 36

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The equivalent expression for the given equation is found as : -5x + 72.

The given expression:

-5(X - 8) + 32

Equivalent expression is found using distributive property:

-5*x -(5)*(-8) + 32

-5x + 40 + 32

-5x + 72

Thus, the equivalent expression for the given equation is found as : -5x + 72.

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Answer:

Perimeter of ΔABC =32.31 units

Area of the triangle ABC = 47.81 sq. unit

Step-by-step explanation:

In triangle ABC

\(\angle A = 60^{\circ}\\\angle C = 45^{\circ}\)

Angle sum property of triangle : The sum of the measures of the all angles of triangle is 180°

\(\angle A + \angle B + \angle C = 180^{\circ}\\60 + \angle B + 45 = 180\\\angle B + 105 = 180\\\angle B = 75^{\circ}\)

Now we are supposed to find the perimeter and the area of the ΔABC

We will use the sine rule to find the lengths of sides BC and AC

Sine rule : \(\frac{Sin A}{BC}=\frac{Sin B}{AC}=\frac{Sin C}{AB}\)

\(\frac{Sin 60}{BC}=\frac{Sin 75}{AC}=\frac{Sin 45}{9}\\BC \times sin(45) = 9 \times sin(60)\\ BC = 11.02\)

\(AC \times sin(45) = 9 \times sin(75)\)

AC = 12.29

Perimeter of ΔABC = AB + BC + AC

Perimeter of ΔABC = 9 + 11.02 + 12.29 =32.31 units

Area by using the sine rule:

Area of the triangle ABC =\(\frac{1}{2} (AB)(BC) sin B\)

Area of the triangle ABC =\(\frac{1}{2} (9)(11) sin(75)\)

 Area of the triangle ABC = 47.81 sq. unit