at the zoo,the ratio of monkeys to gorillas is 5:1​

Answer:

(A) a triangle with a base of 6m and height of 4m:

Area = 1/2 x base x height = 1/2 x 6m x 4m = 12m^2

(B) a parallelogram with a base of 48m and a height of 0.5m:

Area = base x height = 48m x 0.5m = 24m^2

(C) a trapezoid with bases 9m and 3m and height of 4m:

Area = 1/2 x (base1 + base2) x height = 1/2 x (9m + 3m) x 4m = 24m^2

(D) a triangle with a base of 8m and a height of 3m:

Area = 1/2 x base x height = 1/2 x 8m x 3m = 12m^2

So the shapes that have an area of 24 m^2 are A (triangle) and C (trapezoid).

I Hope This Helps!

The areas of the shaded regions are π/3 and 40π

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

Central angle = 120 degrees

Radius = 3 and 4 units

Using the above as a guide, we have the following:

Shaded area = central angle/360 * π * (R - r)²

So, we have

Shaded area = 120/360 * (4 - 3)² * π

Evaluate

Shaded area = π/3

For the second shape, we have

Central angle = 120 degrees

Radius = 10 in

Using the above as a guide, we have the following:

Shaded area = 2 * central angle/360 * π * r²

So, we have

Shaded area = 2 * 72/360 * 10² * π

Evaluate

Shaded area = 40π

Hence, the areas of the shaded regions are π/3 and 40π

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:

38 ft, 41 ft, 44 ft, 47 ft

Step-by-step explanation:

let the first piece be x, then

second piece = x + 3

third piece = x + 3 + 3 = x + 6

fourth piece = x + 6 + 3 = x + 9

sum the 4 together and equate to 170

x + x + 3 + x + 6 + x + 9 = 170, that is

4x + 18 = 170 ( subtract 18 from both sides )

4x = 152 ( divide both sides by 4 )

x = 38

Thus

first piece = x = 38 ft

second piece = x + 3 = 38 + 3 = 41 ft

third piece = x + 6 = 38 + 6 = 44 ft

fourth piece = x + 9 = 38 + 9 = 47 ft

Answer:

\(P(-2<Z<2)=95\%\)

Step-by-step explanation:

From question we are told that

Sample mean \(\=x= 47\)

Standard deviation \(\sigma =7\)

Generally the  X -Normal is given as

      \(Z=\frac{x-\=x}{\sigma}\)

      \(Z=\frac{x-47}{9}\)

Analyzing the range

    \(P(47<x<65) = P(0< z<2.00)\)

    \(P(47<x<65) = 95/2\)

   \(P(47<x<65) = 47.5\%\)

Mathematically

\(Z_1 =\frac{47-47}{9} =0\)

\(Z_2 =\frac{65-47}{9} =2\)

Empirical rule shows that

\(P(-2<Z<2)=95\%\)

Answer:

x = − 5

Step-by-step explanation:

Divide each term by  − 14  and simplify.

Answer: x =5

Step-by-step explanation:

14x/14= 70/14

X = 5

Keep in mind that without the population standard deviation, it is impossible to provide an exact sample size. However, this formula will give you a good starting point.

To find the sample size needed for a 99.5% confidence interval with a margin of error of 1.5, we can use the formula:

n = (Z * σ / E)^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the margin of error.

For a 99.5% confidence interval, the Z-score is approximately 2.807 (from a standard normal distribution table). Since we do not have the population standard deviation (σ), we will need to estimate it using a sample standard deviation or use a conservative approach by assuming the maximum possible value. For now, let's assume we have an estimated standard deviation.

n = (2.807 * σ / 1.5)^2

Solve for n by plugging in the estimated standard deviation (σ) and then round up to the nearest whole number, as you cannot have a fraction of a sample.
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Answer:

22×82=1804. 1804÷18,04

Step-by-step explanation:

✨✨

Answer:

12

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3/3+2/3 = 5/3

Answer is 5

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

       To graph the function g( x) = - f( x 4), we need to start with the graph of the function f( x) = | x| and  also apply the given  metamorphoses.  The function f( x) = | x| represents the absolute value function, which is a V- shaped graph symmetric with respect to the y- axis.  

First, we shift the graph of f( x) = | x| horizontally by 4 units to the left by replacing x with( x 4). This results in f( x 4).  Next, we multiply the entire function by-1, which reflects the graph vertically. This gives us- f( x 4).  Combining these  metamorphoses, we've the function g( x) = - f( x 4). To graph g( x), we can  compass a many points and  also draw the graph by connecting them.

Let's start with the original graph of f( x) = | x| and apply the  metamorphoses

For f( x)  x = -3,-2,-1, 0, 1, 2, 3  

f( x) =  3, 2, 1, 0, 1, 2, 3  For

g( x) = - f( x 4)  x = -7,-6,-5,-4,-3,-2,-1  

g( x) = -3,-2,-1, 0,-1,-2,-3

conniving these points and connecting them, we get a V- shaped graph that's reflected vertically and shifted 4 units to the left wing.

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To find the area of the region $AMCN$, we need to calculate the area of the rectangle $ABCD$ and subtract the areas of the triangles $ABM$ and $ADN$.

Given that the rectangle $ABCD$ has dimensions 8 cm by 4 cm, its area is calculated as length times width: $8, \text{cm} \times 4, \text{cm} = 32, \text{cm}^2$.

Since $M$ is the midpoint of $\overline{BC}$, we can see that $\overline{BM}$ and $\overline{CM}$ are each half the length of $\overline{BC}$. So, $\overline{BM} = \overline{CM} = \frac{1}{2} \times 4 , \text{cm} = 2 , \text{cm}$.

Similarly, $N$ is the midpoint of $\overline{CD}$, so $\overline{DN} = \overline{CN} = \frac{1}{2} \times 8 , \text{cm} = 4 , \text{cm}$.

Now, we can calculate the areas of the triangles $ABM$ and $ADN$. The area of a triangle is given by the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.

For triangles $ABM$, the base is $\overline{AB}$, which is 8 cm, and the height is $\overline{BM}$, which is 2 cm. Thus, the area of triangle $ABM$ is: $\frac{1}{2} \times 8 , \text{cm} \times 2 , \text{cm} = 8 , \text{cm}^2$.

For triangle $ADN$, the base is $\overline{AD}$, which is 4 cm, and the height is $\overline{DN}$, which is 4 cm. Therefore, the area of triangle $ADN$ is: $\frac{1}{2} \times 4, \text{cm} \times 4, \text{cm} = 8, \text{cm}^2$.

Finally, to find the area of the region $AMCN$, we subtract the areas of the triangles $ABM$ and $ADN$ from the area of the rectangle $ABCD$:

$\text{Area of region} , AMCN = \text{Area} , ABCD - \text{Area} , ABM - \text{Area} , ADN = 32 , \text{cm}^2 - 8 , \text{cm}^2 - 8 , \text{cm}^2 = 16 , \text{cm}^2$.

Therefore, the number of square centimeters in the area $AMCN$ is 16.

The area of region $AMCN$ is $48$ square centimetres.

To find the area of region $AMCN$, we can consider that it is composed of two smaller rectangles: $AMCB$ and $ANC$.

$AMCB$ is a rectangle with length $AB = 8$ cm and width $BM = \frac{1}{2} \cdot BC = \frac{1}{2} \cdot 4$ cm (since $M$ is the midpoint of $BC$).

Therefore, the area of $AMCB$ is $8 , \text{cm} \times \frac{1}{2} \cdot 4 , \text{cm} = 16 , \text{cm}^2$.

$ANC$ is also a rectangle with length $AC = 8$ cm and width $NC = \frac{1}{2} \cdot CD = \frac{1}{2} \cdot 8$ cm (since $N$ is the midpoint of $CD$).

Therefore, the area of $ANC$ is $8 , \text{cm} \times \frac{1}{2} \cdot 8 , \text{cm} = 32 , \text{cm}^2$.

Now, add the areas of these two rectangles to find the total area of region $AMCN$:

$16 , \text{cm}^2 + 32 , \text{cm}^2 = 48 , \text{cm}^2$

So, the area of region $AMCN$ is $48$ square centimetres.

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Answer:

$44.40

Step-by-step explanation:

100%-70%=30%

30/100x148=44.40 (discounted price)

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The volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

To find the volume of the container, we need to multiply its length, width, and height. Let's convert the given measurements to meters to ensure consistent units.

The length of the container is 2.76 meters.

The width of the container is 23.5 decimeters, which is equal to 2.35 meters (since 1 decimeter = 0.1 meters).

The height of the container is 196 centimeters, which is equal to 1.96 meters (since 1 meter = 100 centimeters).

Now we can calculate the volume of the container:

Volume = Length × Width × Height

Volume = 2.76 meters × 2.35 meters × 1.96 meters

Volume ≈ 12.9516 cubic meters (rounded to four decimal places)

Therefore, the volume of the container is approximately 12.9516 cubic meters when rounded to the nearest hundredth.

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Answer:

absolute minimum = -749 and

absolute maximum = 467

Step-by-step explanation:

To get the absolute maximum and minimum of the function, the following steps must be followed.

First, we need to find the values of the function at the given interval [-4, 5].

Given the function f(x) = 6x³ − 9x² − 216x + 3

at x = -4;

f(-4) = 6(-4)³ − 9(-4)² − 216(-4) + 3

f(-4) = 6(-64) - 9(16)+864+3

f(-4) = -256- 144+864+3

f(-4) = 467

at x = 5;

f(5) = 6(5)³ − 9(5)² − 216(5) + 3

f(5) = 6(125) - 9(25)-1080+3

f(5) = 750- 225-1080+3

f(5) = -552

Then we will get the values of the function at the crirical points.

The critical points are the value of x when df/dx = 0

df/dx = 18x²-18x-216 = 0

18x²-18x-216 = 0

Dividing through by 18 will give;

x²-x-12 = 0

On factorizing the resulting quadratic equation;

(x²-4x)+(3x-12) = 0

x(x-4)+3(x-4) = 0

(x+3)(x-4) = 0

x+3 = 0 and x-4 = 0

x = -3 and x = 4 (critical points)

at x  = -3;

f(-3) = 6(-3)³ − 9(-3)² − 216(-3) + 3

f(-3) = 6(-27) - 9(9)+648+3

f(-3) = -162-81+648+3

f(-3) = 408

at x = 4

f(4) = 6(4)³ − 9(4)² − 216(4) + 3

f(4) = 6(64) - 9(16)-864+3

f(4) = 256- 144-864+3

f(4) = -749

Based on the values gotten, it can be seen that the absolute minimum and maximum are -749 and 467 respectively

Answer:

3/4 = 0.75

Have a beautiful day!

The quotient when 6+8i is divided by 2i is given by -3i+4.

We know that, complex number \(i^1=-1\).

Given the divisor is = 2i and dividend is = 6+8i

Dividing the dividend by divisor we get,

(6+8i)/2i = 6/2i + 8i/2i = 3/i + 4 \(=\frac{3i}{i^2}+4\) = 3i/(-1)+4 = -3i+4

Hence the quotient is = -3i+4.

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Let P and Q be two complex numbers such that

P = a+bi

Q = c+di

Where a,b,c,d are real numbers and i = sqrt(-1).

This means i^2 = -1.

-------------------

Adding P and Q means

P+Q = (a+bi)+(c+di)

P+Q = a+bi + c+di

P+Q = (a+c) + (bi+di)

P+Q = (a+c) + (b+d)i

As you can see, we just add the corresponding components together.

-------------------

Subtraction is a similar story.

P-Q = (a+bi)-(c+di)

P-Q = a+bi - c-di

P-Q = (a-c) + (bi-di)

P-Q = (a-c) + (b-d)i

We subtract the corresponding components

-------------------

Multiplication is a bit more complicated.

We'll use the FOIL rule

P*Q = (a+bi)*(c+di)

P*Q = a*c + a*di + bi*c + bi*di

P*Q = a*c + ad*i + bc*i + bd*i^2

P*Q = a*c + ad*i + bc*i + bd*(-1)

P*Q = a*c + ad*i + bc*i - bd

P*Q = (ac - bd) + (ad*i + bc*i)

P*Q = (ac - bd) + (ad + bc)i

Unfortunately multiplication isn't as simple as addition or subtraction, but we can at least make a tidy formula for it. You could also use the box method to visually organize the terms into a table to help multiply out P and Q.

Answer:

because they have different stepa

Answer:1212.08 ft

Step-by-step explanation:

Given

Height of Della=5.5 ft

Height of Tower H=1450

angle of elevation \(50^{\circ}\)

Effective height of building for Della=1450-5.5=144.5 ft

From the figure we can write

\(\tan 50^{\circ}=\dfrac{1444.5}{x}\\x=\dfrac{1444.5}{\tan 50^{\circ}}\\x=1212.079\approx 1212.08\ ft\)

Answer: 6 divided by 5 is 1.2

Step-by-step explanation: I used Siri lol

Answer:

1.2 in decimal form. equivalent form-12/10. i really dont know what your asking. so i hope this is what you wanted.

Step-by-step explanation:

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:

Step-by-step explanation:

Given the following scores 3, 7 and 2, we are to find the expression Σ2X-2 and Σ(X-1)²

The value of X's are 3, 7 and 2. Substituting the values we will have;

Σ2X-2 = [2(3)+2(7)+2(2)] - 2

Σ2X-2 = (6+14+4) - 2

Σ2X-2  = 24-2

Σ2X-2  = 22

For  Σ(X-1)²

Σ(X-1)² = (3-1)²+ (7-1)² + (2-1)²

Σ(X-1)² = 2²+6²+1²

Σ(X-1)² = 4+ 36+1

Σ(X-1)² = 41

Σ2X  - 2 = 22 , Σ( X - 1 )^2 = 41

Given : X = 3 , 7 , 2

Σ2X is calculated in the image = 24

Σ2X  - 2 = 24 - 2 = 22

Σ( X - 1 )^2 calculation is shown, it is = 41

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Answer:

Undefined

Step-by-step explanation:

Answer:

$1.82

Step-by-step explanation:

6.60/12 cupcakes=x/1 cupcake

6.60*1=12x

6.60=12x

12/6.60=x

x=1.82

$1.82

Answer:

Step-by-step explanation:

in this kinda question, you need to know that if a line is

parallel to another line, it will have the same slope if it's

perpendicular, it will be negative reciprocal of the slope

thus, if the line is parallel to the one in the question, it will have a slope of 3/4.

and now just substitute the point that is given. (it's a solution of the equation btw)

so -6 = 3/4 (0) + b (the reason we dont include the (-4) is because it will have a different y-interecept, so we need to solve for b)

b=-6.

so y=3/4x - 6

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Answer:

equation 1or 2 divide

3x+y=7

2x+5y=22

or, equation 1 multiple 5

15x+5y=35

2x+5y=22

or,13x=13

therefore x=1 again

value of x put the y in equation 2

2.1 + 5y=22

5y=11

therefore y=11/5