Justine used unit cubes to build a rectangular prism that is 10 units tall and has a volume of 160 cubic units. Larry used half as many unit cubes to build a rectangular prism that is the same height as Justine's prism. What is the area of the base of Larry's prism?

The value of the expression 5(3r - 10) means the product of 5 and the difference of three times r minus 10. If r= 4, the value of the expression is 10.

Mathematical expression is mathematical statement which involves variables, numerical values, mathematical operations, and exponent.

Given the expression in words "the product of 5 and the difference of three times r minus 10"

Three times of 'r' is = 3r

Difference between three times of r and 10 = 3r - 10

The product of 5 and difference between three times of r and 10 = 5(3r - 10)

So the expression is given by, f(r) = 5(3r - 10)

Also the given value of the variable is, r = 4.

Substituting the value in the expression we get,

f(4) = 5(3*4 - 10) = 5*(12 - 10) = 5*2 = 10

Hence the value of the expression when r = 4 is 10.

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Answer:

If you're multiplying the answer would be 454.25.

197.5 x 2.3 = 454.25



The expression that can be used to find the value of x is ∘23sin85∘​/sin55∘, the correct option is A

We are given that;

In triangle DEF, EF=23, DE=x, angleD=85degree, angleF=55degree

Now,

To find the value of x, we can use the law of sines with the given information:

sin85∘x​=sin55∘23​

Solving for x, we get:

x=sin55∘23sin85∘​

Using a calculator, we can approximate x as:

x≈26.6

Therefore, by the given angles the answer will be ∘23sin85∘​/sin55∘

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The z score associated with four cups of coffee is -0.19.

To calculate the z score, we use the formula z = (x - μ) / σ,

where x is the value we want to find the z score for, μ is the mean, and σ is the standard deviation.

In this case, x = 4, μ = 4.76, and σ = 4.18. Plugging these values into the formula, we get:
z = (4 - 4.76) / 4.18
z = -0.19
Therefore, the z score associated with four cups of coffee is -0.19.

Hence,  The z-score of -0.182 represents how many standard deviations away 4 cups of coffee is from the mean number of daily cups of coffee for college student respondents in the survey.

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Answer:

9 cm^2

Step-by-step explanation:

1/2x9x2

4.5x2

9

Hope this helps :)

Answer:

Step-by-step explanation:

We are given with a triangle whose Height is 2 cm and base is 9 cm.

We have to calculate the Area of triangle.

As we know that area of triangle is calculated by,

Area = ½ × base × height

Putting the required values we get,

Area = 1/2 × 2 × 9 (cancel 2 with 2)

Area = 9 cm².

Hence, The area of the triangle is 9 cm².

More Formulas related to area :

[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} {\boxed{\begin{array}{c} \sf Rectangle = Length \times breadth \\ \\ \sf Square = {(Side)}^{2} \\ \\ \sf Trapezium = \dfrac{1}{2} (a+b) h \\ \\ \sf Triangle = \dfrac{1}{2} \times Base \times Height \\ \\ \sf Rhombus = \dfrac{1}{2} \times d_1 \times d_2 \\ \\ \sf Circle = \pi r^2 \\ \\ \sf Parallelogram = Base \times Height \\ \\ \sf Equilateral \: \triangle = \dfrac{ \sqrt{3} }{4} a^2 \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}[/tex]

the percentage reduction in cost is 0%, which means there was no reduction in cost for adults.

What is simple interest?

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

we know that the cost for an adult was not changed in May. Therefore, we can set the original cost equal to the new cost:

x = $22.10

Substituting this value in the equation above, we get:

$22.10 = 22.10 * (100/ (100-p))

Simplifying the equation, we get:

1 = 100 / (100-p)

Multiplying both sides by (100-p), we get:

100-p = 100

Therefore, p = 0.

So, the percentage reduction in cost is 0%, which means there was no reduction in cost for adults.

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Answer:

$768

Step-by-step explanation:

8 x 12 = 96 m²

1 m² = $8.00

96m² x $8.00 = $768

The mean of the heart rates is 9.20

Given that, the heart rates of 36 whales, we need to find the mean of the population,

Mean μ = ∑x / N

N = sample size

x = observed population

Mean μ = 11+10+12+12+8+10+13+11+13+9+11+8+12+6+8+13+5+8+9+8+12+6+9+7+6+8+7+9+9+5+12+9+11+7+8+9 / 36

= 331 / 36

= 9.20

Hence, the mean of the heart rates is 9.20

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The measure of the altitude NE in the triangle CNE for the given similarity  is equal to 4 units.

Here In the attached figure,

B is the unknown vertex where ray AM and DE intersects.

In the triangles,

Triangle ABE ~ Triangle CDE

⇒measure of ∠A = measure of ∠C  __(1)

AE = 15

CE = 5

ME = 12

Let 'x' be the measure of altitude NE.

In ΔAME and ΔCNE,

Measure of ∠A = Measure of ∠C  (from 1)

Measure of ∠AME = Measure of ∠CNE  ( each 90° )

Measure of ∠AEM = Measure of ∠CEN ( vertically opposite angles)

By AAA corollary we have,

ΔAME ~ ΔCNE

In similar triangles corresponding sides are in proportion .

AE / CE = ME / NE

Substitute the values we have,

⇒ 15 /5 = 12/ x

⇒x =12/3

⇒x = 4

⇒NE = 4 units.

Therefore , the length of the altitude NE is equal to 4 units.

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The above question is incomplete, the complete question is:

Use similar triangles to find the length of the altitude.

Triangle ABE ~ Triangle CDE. Find the length of altitude for NE.

Attached figure.

Answer:

7 you would times 6 by 7 to get 42

Answer:

Step-by-step explanation:

Product is 42 after you multiply by

Here you do the reverse:

42 ÷ 6 =

7 is greater than 6 therefore your answer is

There are 56 possible outcomes that contain exactly 3 heads when a coin is flipped 8 times.

To find the number of possible outcomes that contain exactly 3 heads when a coin is flipped 8 times, we can use the formula for combinations.

The total number of possible outcomes when flipping a coin 8 times is 2^8 = 256 (since each flip can result in 2 outcomes: heads or tails).

To calculate the number of outcomes with exactly 3 heads, we need to choose 3 out of the 8 flips to be heads, and the remaining 5 flips to be tails. The number of ways to choose 3 items out of a set of 8 is given by the combination formula:

C(8,3) = 8! / (3! * 5!) = 56

Therefore, there are 56 possible outcomes that contain exactly 3 heads when a coin is flipped 8 times.

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Answer:

It is an obtuse triangle.

Step-by-step explanation:

To determine whether the triangle is right, acute, or obtuse, we can use the Pythagorean Theorem which states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.

Let's first determine which side is the longest.

48 is the largest of the three sides, so we'll use it as the hypotenuse.

Now we can apply the Pythagorean Theorem:

a^2 + b^2 = c^2

where a and b are the shorter sides and c is the hypotenuse.

Plugging in the values, we get:

46^2 + 20^2 = 48^2

2116 + 400 = 2304

2516 = 2304

Since 2516 is greater than 2304, we can see that the triangle is obtuse.

Answer:

Step-by-step explanation:

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The condition for the first dark fringe through a single slit of width w is given by w sin(θ) = λ/2.

The condition for destructive interference at the first dark fringe can be found using the path difference between the two waves.

For the first dark fringe, the path difference between the two waves that pass through the edges of the slit must be half a wavelength:

Δx = λ/2

where Δx is the path difference and λ is the wavelength of the light.

The path difference Δx can be related to the width of the slit w and the angle θ that the diffracted wave makes with the central axis of the slit by:

Δx = w sin(θ)

Therefore, the condition for the first dark fringe can be expressed as:

w sin(θ) = λ/2

The condition for the first dark fringe through a single slit of width w is given by w sin(θ) = λ/2.

This means that if the width of the slit and the wavelength of the light are known, the angle θ at which the first dark fringe occurs can be calculated.

This condition arises due to the interference of the diffracted waves from the edges of the slit. When the path difference between these waves is equal to half a wavelength, the waves interfere destructively and produce a dark fringe.

The first dark fringe is observed at the angle θ for which the path difference between the waves passing through the edges of the slit is equal to λ/2.

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Answer:

x= 4 and y= 2

Step-by-step explanation:

3x+3y= 18 (1)

2y= x (2)

from (1):

x+y= 6

y= 6-x (3)

sub (3) into (2):

2(6-x)= x

12-2x= x

-3x= -12

x= 4 (4)

sub (4) into (3):

y= 6-4

= 2

The values of the trigonometric identities are:

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

We have,

Sin = Perpendicular / Hypotenuse

Cos = Base / Hypotenuse

Tan = Perpendicular / Base

Now,

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

And,

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

Thus,

The values of the trigonometric identities are:

Sin X = 5/13

Cos X = 12/15

Tan X = 5/12

Sin M = 12/13

Cos M = 5/13

Tan M = 12/5

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The total surface area of the prism is 156 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of prism is expressed as;

SA = 2B + ph

where p is the perimeter of the base

B is the base area

h is the height of the prism

Base area = 1/2 bh

h = √5²-4²

= √25-16

= √9 = 3

area = 1/2 × 4×3

= 6 cm²

Perimeter of the base = 3+4+5 = 12 cm

height = 12cm

SA = 2 × 6 + 12 × 12

= 12 + 144

= 156 cm²

therefore the surface area of the prism is 156 cm²

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Answer:

135 degrees

Step-by-step explanation:

angle 3 and 7 are corresponding meaning that they are equal so we find the measure of angle 3

to do this we subtract the measure of 4 which is 55 from 180

180-55

135

hopes this helps

This looks like a quadratic equation!

Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

Answer: Let's first rewrite the equation in the standard form (where the coefficients of x2 and x, as well as the constant term all have absolute values greater than 0)

ax^2 + bx + c = 0

And then use the Quadratic Formula to solve for x.

x = (-b ± √[b^2 - 4ac])/2a

Where a, b, and c are the coefficients of x^2, x, and 1, respectively.

Now, we just need to substitute the constants and solve for x!

-8x^2 + 10x + 15 = 0

a = -8

b = 10

c = 15

x = (-10 ± √[100 - 4(-8)(-15)])/2(-8)

x = (-10 ± √[100 - 240])/-16

x = (-10 ± √-140)/-16

x_1 = -7/16

x_2 = -7/16

Since x must be a real number, we can disregard x_2 and therefore the value of x is -7/16.

So the value of x is -7/16!

If -7/16 isn't the answer you were looking for, then try it in decimal form.

wich is -0.4375

Step-by-step explanation:

The center and the radius of the circle of equation 3x² + 3y² + 12x + 18y - 36 = 0 are given as follows:

A. (-2, -3), r = 5.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation of the circle in this problem is given as follows:

3x² + 3y² + 12x + 18y - 36 = 0

Simplifying by 3, we have that:

x² + y² + 4x + 6y - 12 = 0.

Completing the squares, we have that:

x² + 4x + y² + 6y = 12

(x + 2)² + (y + 3)² = 12 + 2² + 3²

(x + 2)² + (y + 3)² = 25.

Hence the correct option is given by option A.

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Answer:

36.59

Step-by-step explanation:

The sample size for estimate the proportion of families in a certain area that are living below the poverty level is equals to the 318.75.

The standard error is a statistic term that is the standard deviation of its sampling distribution or an estimate of that standard deviation. In case of sample mean, it is called the standard error of the mean. Formula of standard mean is

[tex] SE =\sqrt{ \frac{\hat p (1 - \hat p)}{n}} [/tex]

where, n--> sample size

We have a simple random sample for estimate the proportion of families,

Sample proportion = 0.15

Standard error = 0.02

We have to determine the sample size for the standard error of the estimate is .02.

Here, SE = 0.02, \hat p = 0.15

Using the standard score formula,

[tex] 0.02 =\sqrt{ \frac{0.15 (1 - 0.15)}{n}} [/tex]

Squaring both sides

[tex] 0.02² = \frac{0.15 ×0.85 }{n} [/tex]

[tex] 0.0004 = \frac{0.1275 }{n} [/tex]

=> n = 318.75

Hence, required value is 318.75.

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According to the table, 18% of Mountain View residents polled supported Olunloyo.

In the given table, the percentage of Mountain View residents who supported Olunloyo can be found by looking at the value in the intersection of "Mountain View" row and "Olunloyo" column, which is 0.18 or 18%.

To understand how this value is calculated, keep in mind that the values in the table represent relative frequencies.

A relative frequency is the fraction or proportion of a group that belongs to a specific category or has a specific feature. In this case, the groups are Cherry Hill and Mountain View residents, and the categories are the candidates they support.

So, the percentage of Mountain View residents polled who supported Olunloyo can be calculated as:

(0.18/0.48) x 100% = 37.5%

Therefore, 18% of the residents from Mountain View supported Olunloyo, according to the given table.

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Your question seems incomplete, the probable complete question is:

A survey of two communities asked residents which candidate they supported for a local election. the survey data are shown in the relative frequency table. what percentage of mountain view residents polled supported olunloyo?

The solution of the given system of equations are 1) (2, 1) and 2) (4, 3)

Given are two system of linear equation, we need to solve it,

1) y = 6x-11......(i)

-2x-3y = -7.........(ii)

Solution -

Put eq(i) in eq(ii),

-2x-3(6x-11) = -7

2x + 18x - 33 = 7

20x = 40

x = 2

Put x = 2, in eq(i)

y = 6(2)-11

y = 12-11

y = 1

The solution is (2, 1)

2) 2x-3y = -1......(i)

y = x-1.........(ii)

Solution -

Put eq(ii) in eq(i),

2x-3(x-1) = -1

2x-3x+3 = -1

-x = -4

x = 4

Put x = 4, in eq(ii)

y = 4-1

y = 3

The solution is (4, 3)

Hence, the solution of the given system of equations are 1) (2, 1) and 2) (4, 3)

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The equation of a line in standard form is Rx + Py = - RP

From the question, we have the following parameters that can be used in our computation:

x-intercept (−P, 0) and y-intercept (0, −R).

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

In this case,

c = -R

So, we have

y = mx - R

Using the other point, we have

0 = -Pm - R

So, we have

-Pm = R

Evaluate

m = -R/P

So, we have

y = -R/Px - R

This gives

Py = -Rx - RP

Add Rx to both sides

Rx + Py = - RP

Hence, the equation is Rx + Py = - RP

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Eliza took home 35/24 pans of fruit bars.

The problem involves finding the number of fruit bars left after a certain fraction has been consumed and then calculating how much of the remaining fruit bars were taken home using another fraction.

Here we have

Eliza brought 6 pans of homemade fruit bars to school.

Her classmates ate 5/12 of each pan.

The total amount of fruit bars they consumed is:

=>  6 pans x 5/12 = 2.5 pans

So Eliza had 6 - 2.5 = 3.5 pans of fruit bars left.

Eliza gave 1 whole pan of the leftover fruit bars to the school's secretaries and took the rest home.

Leftover bars = 3.5 pans - 1 pan = 2.5 pans

To find the number of the fruit bars she took home, multiply the number of pans by the amount that wasn't eaten, which is:

=> 2.5 pans x 7/12 = 35/24 pans

Therefore,

Eliza took home 35/24 pans of fruit bars.

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The expression for value of x is (23 sin55)/sin85

Hence, Option C is correct.

In the given figure,

Angle D = 85° and Angle F = 55°

length of DE = x and length of EF = 23

Apply sine rule

SinD/EF = SinF/ED

Put the given values shown in the figure,  

Sin85/23 = sin55/x

Hence,

⇒x = (23 sin55)/sin85

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The distance between the points (-6,7) and (-1,1) is  7.81 units

We know that the distance formula between two points (x₁, y₁) and (x₂, y₂) is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

We need to find the distance between the points (-6,7) and (-1,1)

Let (x₁, y₁) = (-6, 7)

and (x₂, y₂) = (-1, 1)

Using above distance formula, the distance between the points (-6,7) and (-1,1) would be,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(1 - 7)² + (-1 - (-6))²]

d = √[(1 - 7)² + (-1 + 6)²]

d = √[(-6)² + (5)²]

d = √[36 + 25]

d = √(61)

d = 7.81 units

This is the required distance.

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If point is plotted at (3, 5) and (3, -6), then the distance between the two points plotted is (b) 11 units.

The two points plotted are (3, 5) and (3, -6). We see that both the points have the same x-coordinate, which means that both points lie on the same "vertical-line" which is parallel to the y-axis.

The distance between these two points is the vertical distance between their y-coordinates, which is:

The "y-coordinate" of the points are 5 and -6,

So, the distance will be = |5 - (-6)| = 11 units,

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

A graph with the x-axis starting at -10, with tick marks every one unit up to 10. The y-axis starts at -10, with tick marks every one unit up to 10.

A point is plotted at (3, 5) and at (3, -6).

What is the distance between the two points plotted?

(a) 1 unit

(b) 11 units

(c) -11 units

(d) -1 unit

106.8 is the population variance.

To calculate the population variance, we use the formula:

[tex]s^{2}[/tex] = Σ [[tex](xi-u)^{2}[/tex]] / N,

where xi is the ith observation, u is the population mean, and N is the population size.

First, we need to calculate the population mean:

u = (38 + 26 + 13 + 41 + 22) / 5 = 28.

Next, we calculate the sum of squares:

Σ [[tex](xi-u)^{2}[/tex]] = [tex](38-28)^{2}+ (26-28)^{2}+(13-28)^{2}+(41-28)^{2}+(22-28)^{2}[/tex]

= 100 + 4 + 225 + 169 + 36

= 534.

Finally, we divide by the population size:

[tex]s^{2}[/tex] = Σ [[tex](xi-u)^{2}[/tex]] / N = 534 / 5 = 106.8.

Therefore, the population variance is 106.8.

The closest choice to this answer is 106.8, which is the first option. So the answer is 106.8.

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Answer:

4 and 5 or 3 and 6

Step-by-step explanation:

Bcz the answers are alternate angles and are in the interior

Answer:

B. ∠4 and ∠∠5

Step-by-step explanation:

Alternate interior angles lie inside the coplanar lines(in this case the lines b and c ) and they are on opposites sides of the transversal(which is line a ).

The only option that has both of these are ∠4 and ∠∠5