Mr. Garcia gave his students a biology test last week.Here are the test scores for each of the fifteen students.Test scores938398899791838692908884858291(b) Construct a histogram for the data.(a) Complete the grouped frequency distribution forthe data. (Note that the class width is 5.)FrequencyTest scores7-6+79 to 835+84 to 88Frequency0.0043+89 to 932+1194 to 980-79 1083941 98844 to 58 89 to 93Test scoresx5?

You can read a pie chart as follows

Looking at the given pie chart.

The budget for Research is arounf 1/6

The budget for Engineering is around 2/6

The budget for Support is around 1/8

The budget for media and marketing are 1/16 each

The budget for sales is around 3/16

a) The department that has one eight of the budget is Support.

b) The budgets for sales and marketing together add up to

Multiply it by 100 to express it as a percentage

25% of the budget correpsonds to sales and marketing

c) The budget for media looks around one third the budget for research, to determine the percentage of budget that corresponds to media, divide the budget of research by 3

The budget for media is 6%

The seat back cushion is a cuboid. The surafce area can be calculated below

We can see that the y-intercept would be (0,-16) since this is the result of replacing x=0 in the function.

We can also find the x-intercepts solving the equation 0=2x^2+4x-16. Doing so, we have:

The graph that satisfies the conditions we have found previously is the option A.

We have the following:

the value of pi / 2 is not defined

The circumference of a circle is given by the following formula

where r represents the radius.

The ratio between two circumferences is equal to the ratio of the radius.

The area of a circle is given by the following formula

Then, the ratio between two circle areas is equal to the square of the ratio of the radius, which is the square of the ratio between the circumferences.

Then, applying this relation in our problem, the ratio between the areas is:

The ratio between the areas is 25/4.

Answer:

The amount of interest she will be paid in the first 3 years is;

Explanation:

Given that Lashonda deposits $500 into an account that pays simple interest at a rate of 6% per year. for the first 3 years;

Recall the simple interest formula;

substituting the given values;

Therefore, the amount of interest she will be paid in the first 3 years is;

ANSWER

9933

EXPLANATION

We have the number 9932.8.

We want to round it to the nearest integer.

An integer is a number that can be written without decimal or fraction.

To do that, we follow the following steps:

1. Identify the number after the decimal

2. If the number is greater than or equal to 5, round up to 1 and add to the number before the decimal.

3. If the number is less than 5, round down to 0.

Since the number after the decimal is 8, we therefore have that:

First, let's calculate the number of different hands of 5 cards that can be made, using a combination of 52 choose 5:

(a standard deck card has 52 cards)

Now, let's calculate the number of hands that have 4 aces. Since the fifth card can be any of the remaining 48 cards after picking the 4 aces, there are 48 possible hands that have 4 aces.

Then, the probability of having a hand with 4 aces is given by the division of these 48 possible hands over the total number of possible hands of 5 cards:

The probability is 1/54145.

Notice that

400,000 = 0.4 million

That's why the equation that models that information has the factor 0.4, since it expresses the result in millions of females.

Now, we need to notice that t, in the expression 0.4t + 6.1, is the number of years passed since 2009. So, in the year 2024, we have:

t = 2024 - 2009 = 15

Therefore, the number of females enrolled in 2024 can be estimated to be:

y = (0.4 * 15 + 6.1) million

y = (6 + 6.1) million

y = 12.1 million

Now, to determine the year when 12.9 million females will be enrolled, we first need to find t corresponding to y = 12.9, and then add it to the year 2009.

y = 0.4t + 6.1​

12.9 = 0.4t + 6.1

12.9 - 6.1 = 0.4t

6.8 = 0.4t

t = 6.8/0.4

t = 68/4

t = 17

Therefore, the year when it happens will be:

2009 + 17 = 2026

Given

Solution

Standard from of a parabola

The standard form equation of a line is expressed as

Ax + By = C

where

A, B and C are real numbers and A and B are not both zero. From the information given,

the line passes through(- 2, 5) and slope = - 4

We would find the y intercept of the line, c by substituting slope, m = - 4, x = - 2 and y = 5 into the slope intercept equation which is expressed as

y = mx + c

Thus, we have

5 = - 4 * - 2 + c

5 = 8 + c

c = 5 - 8 = - 3

Thus, the equation of the line in the slope intercept form is

y = - 4x - 3

We would convert it to standard form. Thus, we have

y + 4x = - 3

4x + y = - 3

Thus, the equation in standard form is

4x + y = - 3

By using some exponent properties, we will see that the expression can be written as:

a^6

Here we need to use some exponent properties, these are:

Here we have the expression:

(a^(-1)*a^(-2))^(-2)

Using the third property we can write:

(a^(-1)*a^(-2))^(-2) = (a^(-1 - 2))^(-2) = (a^(-3))^(-2)

Now we use the first property:

(a^(-3))^(-2) = a^(-3*-2) = a^6

That is the expression simplified.

Learn more about exponents:

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A rhombus is a quadrilateral with 4 congruent sides.

For the Rhombus ABCD given

Also,

Also,

From the image given, the data shows that

We can observe that

Thus, from the above we can say that;

Hence

Yes, the given information is enough to prove that ABCD is a parallelogram.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{y}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{1}}} ~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{3}\implies \cfrac{2-y}{7}=3 \\\\\\ 2-y=21\implies -y=19\implies y=\cfrac{19}{-1}\implies y=-19[/tex]

In the given equation A, we can (A) subtract the same quantity from both sides.

So, obtain equation B from equation A:

We can subtract (2x) from both sides to get equation B as follows:

Therefore, in the given equation A, we can (A) subtract the same quantity from both sides.

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To answer this question we have to identify the elements of the inequality.

1. The difference of a number and 2 is represented by the expression: x-2.

2. Twice the difference (...) is represented by the expression: 2(x-2).

3. At least is represented by the sign greater than or equal to ≥.

4. The result is -28.

By putting these all together we obtain the inequality:

It means that the answer is 2(x-2) ≥ -28.

Solution;

x=-9

The Pythagorean theorem states:

where a and b are the legs and c is the hypotenuse of a right triangle.

Substituting with c = 9 and a = 5, we get:

Answer: 100

Step-by-step explanation:

$1 =100 pennies

Answer: Option 4: c=13.8m, A=28.8°, B=40.1°

Explanation:

From the information given,

the known sides are a = 7.1 and b = 9.6

the known angle is C = 111.1

We would find side c by applying the cosine rule which is expressed as

c^2 = a^2 + b^2 - 2abCosC

By substituting the given values into the formula,

c^2 = 7.1^2 + 9.6^2 - 2 x 7.1 x 9.6Cos111.1

c^2 = 50.41 + 92.16 - 136.32Cos111.1

c^2 = 142.57 - 136.32Cos111.1 = 191.6448

c = √191.6448 = 13.8436

c = 13.8

To find angle A, we would apply the sine rule which is expressed as

a/SinA = c/SinC

Thus,

7.1/SinA = 13.8436/Sin 111.1

By cross multiplying, we have

13.8436SinA = 7.1Sin111.1

SinA = 7.1Sin111.1/13.8436 = 0.4785

Taking the sine inverse of 0.4785,

A = 28.8

Recall, the sum of the angles in a triangle is 180. Thus,

A + B + C = 180

28.8 + B + 111.1 = 180

139.9 + B = 180

B = 180 - 139.9

B = 40.1

Option 4: c=13.8m, A=28.8°, B=40.1°

The height of the tree is 13.82 m

Step - by - Step Explanation

What to find? Height of the tree.

Given:

• Angle of elevation = 62,°

• Eye-level above the ground =160cm

• Distance away from the tree = 6.5m

We need to first sketch the problem, to have a clearer picture of the question.

Change 160cm to meter

160 cm = 160/100 = 1.6 m

Height of the tree = 1.6 + x

We need to find the value of x.

From the sketch above;

Opposite =x

Adjacent =6.5

θ= 62°

Using the trigonometric ratio;

Substitute the values.

Cross-multiply.

x=6.5tan62°

x = 12.22 m

Height of the tree = 1.6 m + 12.22m

Height of the tree = 13.82 m

OR

Height of the tree = 1382 cm approximately.

Since we have 5 girls and their parents give each other $10, they have in total $50.

Now, let x be the number of pizzas they buy, since each pizza cost $7.25 the total cost for x pizzas is:

this should be less or equal to $50 (otherwise the girls go over budget), then the inequality that represents this situation is:

Now, solving the inequality we get:

Therefore, they can buy a maximum of 6 pizzas without going over budget.

The angles sum up to give 180°

Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.

We can also have a 90 degree and 2 acute angle in a triangle.

Examples

The angles sum up to give 180°

Only one of the angles can be an obtuse angle, we can;t have two bothuse angle in a triangle. BUT we can have two acute angles and one obtuse angle in a triangle.

We can also have a 90 degree and 2 acute angle in a triangle.

Examples

650 --- total

650*.68=442

442 students ate green bean casserole

.68 represents the percentage

so for example, if they asked me for 50% of 1000

we need to multiply 1000*0.5

if they asked for 60% we will multiply 1000*0.6

To know if the point is on the circle, we mus calculate the distance between the point and the origin.

For the first option, we have:

- (2, √21)

and the origin

- (0, 0)

Then, we must replace the two points in the distance formula:

Knowing that the distancie is 5 we can affirm that the point is on the circle because the radius is 5.

Finally, the answer is

The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:

Replacing with the points (-8, 3) and (0,1) we get:

The linear regression model is

Where

R is the total annual revenue (dependant variable)

t is the time, in years, since 1/31/02 (independent variable)

To predict the annual revenue for the period ending 1/31/10, the first step is to determine the value of t. Considering that t=0 is the first recorded year (1/31/02), the value of t corresponding to period 1/31/10 is the number of years passed since, including 2002, which is 9 years.

So you have to calculate R for t=9. Replace the formula with t=9 and calculate the corresponding value of R

R≈437 billion dollars