Create an expression that has the same value as (6x-4) + (x + 5).
Write the correct numbers from the list in the blank boxes. Each number
may be used once, more than once, or not at all.

The area of the diagram, to the nearest square centimeter, is 37 cm².

Lets say diagram is,

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The diagram is composed of two rectangles and a quarter circle. Let's first calculate the area of the rectangles.

[tex]Area\ of\ rectangle\ 1\ = length\ \times width\ = 5 cm \times 3 cm = 15cm^2\\Area\ of\ rectangle\ 2 = length\ \times width = 5 cm \times 3 cm = 15cm^2\\[/tex]

The total area of the two rectangles is,

Total area of rectangles = Area of rectangle 1 + Area of rectangle 2

Total area of rectangles = [tex]15 cm^2 + 15 cm^2[/tex]

Total area of rectangles = [tex]30 cm^2[/tex]

Next, let's calculate the area of the quarter circle. The radius of the circle is 3 cm (which is half of the width of the rectangles). The formula for the area of a circle is,

[tex]Area\ of\ circle = \pi \times radius^2[/tex]

Since we have a quarter circle, we need to divide the result by 4. Therefore, the area of the quarter circle is,

[tex]Area\ of\ quarter\ circle = \frac{\pi}{4} \times 3^2\\Area\ of\ quarter\ circle = \frac{\pi}{4} \times 9\\Area\ of\ quarter\ circle = 7.07cm^2\\[/tex]

Finally, to find the total area of the diagram, we add the area of the two rectangles and the area of the quarter circle:

Total area of diagram = Total area of rectangles + Area of quarter circle

Total area of diagram = [tex]30 cm^2 + 7.07 cm^2[/tex]

Total area of diagram = [tex]37.07 cm^2[/tex] (rounded to two decimal places)

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The area of the diagram is approximately 32.77 centimeters² to the nearest square centimeter.

In math, region is a proportion of the size of a two-layered surface or locale. It is how much space inside a shut shape or figure, and it is normally estimated in square units, for example, square meters, square centimeters, square inches, or square feet.

To find the area of the diagram, we need to find the area of each of the two rectangles and the quarter circle, and then add them up.

The two rectangles have dimensions of 5 cm by 3 cm and 5 cm by 3 cm, respectively. so, area of each rectangle is:

Area of rectangle = length x width

Area of rectangle 1 = 5 cm x 3 cm = 15 cm²

Area of rectangle 2 = 5 cm x 3 cm = 15 cm²

To find the area of the quarter circle, we need to first find the radius. The radius is half of the diameter, which is equal to the length of one side of the rectangle. So the radius is:

Radius = 3 cm/2 = 1.5 cm

The area of the quarter circle is one-fourth the area of the full circle, which is:

area of quarter circle = 1/4 x π x radius²

area of quarter circle = 1/4 x π x (1.5 cm)² ≈ 1.77 cm² (rounded to two decimal places)

To find the total area of the diagram, we add the areas of the two rectangles and the quarter circle:

Total area = Area of rectangle 1 + Area of rectangle 2 + Area of quarter circle

Total area = 15 cm² + 15 cm² + 1.77 cm² ≈ 32.77 cm²

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The solid that could have resulted in a rectangular cross-section when cut by a plane perpendicular to its base is a rectangular prism.

We have,

A rectangular prism has a rectangular base and it's top and bottom faces are parallel and congruent to the base.

When cut by a plane perpendicular to its base, the cross-section will always be a rectangle, which is congruent to the base.

Other solids such as cones, cylinders, pyramids, spheres, or irregular shapes cannot have a rectangular cross-section when cut by a plane perpendicular to their base.

Thus,

The solid that could have resulted in a rectangular cross-section when cut by a plane perpendicular to its base is a rectangular prism.

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By answering the presented question, we may conclude that As a result, the slope of [tex]y_3[/tex] = -4(x - 5) is -4.

The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x).

The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b.

The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7). The slope of the line is m. b is b at the y-intercept, and (0, b).

The above equation is in point-slope form: y - [tex]y_1[/tex]= m(x - [tex]x_1[/tex]), where ([tex]x_1[/tex], [tex]y_1[/tex]) is a point on the line and m is the slope.

We can see by comparing the provided equation to the point-slope form that [tex]x_{1} ,y_1[/tex]) = (5, 3) and m = -4.

As a result, the slope of [tex]y_3[/tex] = -4(x - 5) is -4.

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The answers to all parts is shown below.

We have,

An oceanographer claims that the mean dive duration of a North Atlantic right whale is minutes.

a) Now, the hypothesis are

[tex]H_0[/tex] : [tex]\mu[/tex] = 11.3

and, [tex]H_\alpha[/tex] : [tex]\mu[/tex] ≠ 11.3

So, the claim is Null Hypothesis

b) t= (x- [tex]\mu_0[/tex])/ (s/ √n)

t= (12.2-11.3)/ (2.2/ √34)

t= 2.39

P value = 0.023

c) Reject [tex]H_0[/tex] because the p value is not greater than α.

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The hypotheses for a two-tailed test, would be A. H0: μ = 1.9 mg ( null hypothesis)

H1: μ ≠ 1.9 mg (alternative hypothesis)

The null hypothesis (H0): The population mean of mercury content in compact fluorescent bulbs is equal to 1.9 mg.

Alternative hypothesis (Ha): The population mean of mercury content in compact fluorescent bulbs is not equal to 1.9 mg.

When put into symbols, this becomes H0: μ=1.9 mg vs. H1: μ ≠ 1.9 mg.

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If the number of students who participated in art decreased by 5, the total number of students the principal would have expected to keep the proportion of students who participated in art the same is (1/2)x + 5.

what is principle?

A fundamental truth, law, or doctrine, such as the principle of gravity or the principles of mathematics.

To keep the number of students who participated in art proportional to the total number of students surveyed, the decrease in the number of students who participated in art must be proportional to the total number of students surveyed.

Let's assume that the total number of students surveyed is "x". If "y" students participated in art, then the proportion of students who participated in art is y/x.

If the number of students who participated in art decreased by 5, then the new number of students who participated in art would be y-5. The new proportion of students who participated in art is (y-5)/x.

To keep the proportion of students who participated in art the same, we can set the two proportions equal to each other:

y/x = (y-5)/x

Solving for "y", we can cross-multiply and simplify:

y = (y-5)

y = (1/2)x

Therefore, if the number of students who participated in art decreased by 5, the total number of students the principal would have expected to keep the proportion of students who participated in art the same is (1/2)x + 5.

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The missing part in the first triangle is 14

The missing part in the second triangle is 13.

The Pythagorean theorem is a fundamental theorem in geometry that applies specifically to right triangles.

According to Pythagorean theory, the square of the length of a right triangle's hypotenuse is equal to the sum of the squares of its legs.

For the first triangle as shown;

16^2 = 8^2 + t^2

t = √16^2 - 8^2

t = √192

t = 14

For the second triangle;

w= √8^2 + 10^2

w = 13

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The solution to the quadratic equation is;

x = -2 ± √27/5

We can see that the equation that we should solve by the method of completing the square is given by;

5x^2 + 20x – 7 = 0

Dividing through by 5 we have;

x^2 + 4x - 7/5 = 0

Thus;

x^2 + 4x = 7/5

When we add 2^2 to both sides to complete the square we have;

(x + 2)^2 = 7/5 + 4

(x + 2)^2 =7 + 20/5

(x + 2)^2 =27/5

x = -2 ± √27/5

This is how the equation that we have can be solved by completing the square method.

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The required triple integral of 1 over the sphere x²+ y²+ z² = 1 is equal to 4π.

To evaluate the triple integral of 1 over the sphere x² + y² + z² = 1, we can use spherical coordinates. The volume element in spherical coordinates is given by:

dV = ρ² sin(φ) dρ dφ dθ

where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis in the xy-plane).

The equation of the sphere can be rewritten in terms of spherical coordinates as:

ρ² = 1

Using this, we can set up the integral as follows:

∫∫∫ 1 dV = [tex]\int_0^{2 \pi} \int_0^{ \pi} \int_0^1 \rho^2 sin(\phi) d\rho d\phi d\theta[/tex]

We can integrate ρ² with respect to ρ from 0 to 1, sin(φ) with respect to φ from 0 to π, and 1 with respect to θ from 0 to 2π:

∫∫∫ 1 dV = [tex]\int_0^{2 \pi} \int_0^{ \pi} \int_0^1 \rho^2 sin(\phi) d\rho d\phi d\theta[/tex]

= 4π

Therefore, the triple integral of 1 over the sphere x²+ y²+ z² = 1 is equal to 4π.

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Answer:The answer is

A

Step-by-step explanation:

Answer:

9 laps takes 5 minutes 25 seconds.

Step-by-step explanation:

Here is given:

4 laps takes 6 minutes 12 seconds.

We have to find how long 1 lap takes.

4/4 6/4 12/4 --> 1 lap takes 2 minutes 33 seconds.

Now, multiply each by 9 because you want to find 9 laps, so:

1x9 2x9 33x9 --> 9 laps takes 5 minutes 25 seconds.

Hope this helps :)

For the given pyramid the lateral area and surface area values are obtained to be 313.536 cm² and 479.714 cm² respectively.

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.

To find the lateral and surface area of a hexagonal pyramid with height 12 cm, base length 8 cm, and radius of the hexagon 6.93 cm, we can follow these steps -

Find the apothem of the hexagonal base.

The apothem is the distance from the center of the base to the midpoint of a side.

Since the radius of the hexagon is given as 6.93 cm, we can use the Pythagorean theorem to find the apothem -

apothem = √(radius² - (side/2)²)

= sqrt(6.93² - (8/2)²)

= √(44.9769 - 16)

= √(28.9769)

= 5.39 cm

Find the slant height of the pyramid.

The slant height is the distance from the apex to the midpoint of a side of the base.

We can use the Pythagorean theorem to find the slant height -

slant height = √(height² + apothem²)

= √(12² + 5.39²)

= 13.064 cm

Find the lateral area of the pyramid.

The lateral area is the sum of the areas of the triangular faces.

Each face is an isosceles triangle with base length 8 cm and height equal to the slant height.

Therefore, the area of each face is -

area of face = (1/2) × base × height

= (1/2) × 8 × 13.064

= 52.256 cm²

There are 6 faces in total, so the lateral area is -

lateral area = 6 × area of face

= 6 × 52.256

= 313.536 cm²

Find the surface area of the pyramid.

The surface area is the sum of the lateral area and the area of the base.

The area of a regular hexagon is given by the formula -

area of hexagon = (3 × √(3) / 2) × side²

Since the side length of the hexagon is 8 cm, we can calculate the area of the base -

area of base = (3 × √(3) / 2) × 8²

= 96 × √(3)

= 166.178 cm²

Therefore, the surface area of the pyramid is -

surface area = lateral area + area of base

= 313.536 + 166.178

= 479.714 cm²

Therefore, the lateral area of the pyramid is 313.536 cm² and the surface area is 479.714 cm² (rounded to the nearest thousandth).

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The number of inches apart that the four bolts will be along the circumference of the metal plate shown in the figure is 9.425 inches.

The circumference refers to the total distance around a circle.

The circumference can determined using the following formula.

Circumference = 2πr

Diameter of the circle = 12 inches

Radius = 12/2 inches = 6 inches

Circumference = 2 x 22/7 x 6

= 37.7 inches

The number of bolts along the circumference = 4

Distance between the four bolts = 9.425 inches (37.8 ÷ 4)

Thus, using division operation, the distance apart of the four bolts is 9.425 inches.

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Answer: 130

Step-by-step explanation:

First find the area of the square: 10*10=100

Then, find the area of the triangle: (10*6)/2=60/2=30

Finally, add the 2 areas together: 100+30=130

Therefore the answer is 130.

Answer:33

Step-by-step explanation:

Since John has 6 fewer cards than Juan the equation is 24-6=18

Tyler has 15 more than John (18) so the equation is 15+18=33

The answer of the given question based on the binomial distribution is ,  the mean is 77.5 , the variance is 29.975 , the standard deviation is 5.48.

A variance is a measure of how much a random variable (such as a set of data) deviates from its expected value, or mean. It is defined as the average squared difference between each observation in the dataset and the mean of the dataset.

In other words, the variance measures how spread out the data is. A low variance means that the data is clustered around the mean, while a high variance means that the data is more spread out.

The mean of binomial distribution is given μ = np. Therefore, for n = 125 and p = 0.62, we have:

μ = np = 125 × 0.62 = 77.5

So the mean is 77.5 (rounded to the nearest tenth).

The variance of a binomial distribution is given by σ² = np(1-p). Therefore, for n = 125 and p = 0.62, we have:

σ² = np(1-p) = 125 × 0.62 × (1 - 0.62) = 29.975

So the variance is 29.975 (rounded to the nearest tenth).

The standard deviation of a binomial distribution is the square root of the variance, so for the same values of n and p, we have:

σ = √(np(1-p)) = √29.975 = 5.48

So the standard deviation is 5.48 (rounded to the nearest hundredth).

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Answer:

The answer is 68114.29 to 2d.p

Step-by-step explanation:

Area of figure =Area of 2semi circle +Area of Rectangle

r=d/2=160/2=80ft

A=pir²+L×B

A=22/7×80²+160×300

A=20114.29+48000

A=68114.29 to 2d.p

The radius of a circle with an area of 32π cm² include the following: 4√2 centimeters.

In Mathematics and Geometry, the area of a circle can be calculated by using this mathematical equation (formula):

Area = πr²

Where:

r represents the radius of a circle.

By substituting the given parameters into the formula for the area of a circle, we have the following;

32π cm² = π × r²

r² = 32

Radius, r = √32

Radius, r = 4√2 centimeters.

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answer is
180 < 181 < 182

……….

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The correct answer is B. The mean would decrease in value to about 17.1 inches.

Step-by-step explanation:

To find out how adding a new plant with a height of 13 inches would impact the mean height of the 15 plants, we can follow these steps:

To find out how adding a new plant with a height of 13 inches would impact the mean height of the 15 plants, we can follow these steps:Find the current mean height of the 14 plants:

mean = (12 + 14 + 15 + 15 + 16 + 16 + 16 + 17 + 18 + 18 + 19 + 20 + 22 + 25) / 14

= 221 / 14

≈ 15.8 inches

Add the new plant with a height of 13 inches to the list.

Add the new plant with a height of 13 inches to the list.Recalculate the mean height of the 15 plants:

mean = (12 + 13 + 14 + 15 + 15 + 16 + 16 + 16 + 17 + 18 + 18 + 19 + 20 + 22 + 25) / 15

= 236 / 15

≈ 15.7 inches

The mean height of the 15 plants after adding the new plant would be approximately 15.7 inches. This means that the mean would decrease in value from about 15.8 inches to about 15.7 inches. Therefore, the correct answer is B. The mean would decrease in value to about 17.1 inches.

The golf ball will hit the pavement after approximately 2.165 seconds.

A function is a rule that corresponds each input value from the domain to precisely one output value from the target set (called the range).

To find when the golf ball hits the pavement, we need to find the value of t when the height h is equal to zero, since the golf ball will be at the pavement at that point.

So we can set h = 0 in the given function and solve for t:

0 = -16t² + 75

Adding 16t² to both sides, we get:

16t² = 75

Dividing both sides by 16, we get:

t² = 4.6875

t ≈ 2.165 seconds or t ≈ -2.165 seconds

Time cannot be negative, hence the unfavourable outcome can be disregarded. Therefore, the golf ball will hit the pavement after approximately 2.165 seconds.

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Answer:

A

Step-by-step explanation:

each input has it’s own output value

Step-by-step explanation:

to find the area you first have to seperate the shape into the triangle on the bottom and the trapezoid on the top. to find the area of the triangle its

[tex]3 \times 2 - 2 \times 2 \div 2 - 1 \times 2 \div 2 = 6 - 2 - 0.5 = 6 - 2.5 = {3.5cm}^{2} [/tex]

then to find the area of the trapezoid its

[tex](4 + 6) \div 2 \times 2 = 10 \div 2 \times 2 = 5 \times 2 = {10cm}^{2} [/tex]

then add both of them together and its 13.5 cm squared.

Answer:

6

Step-by-step explanation:

substitute x = 2 into f(x) , that is

f(2) = 2(2) + [tex]\frac{1}{2}[/tex] (2)² = 4 + [tex]\frac{1}{2}[/tex] (4) = 4 + 2 = 6

Answer:

701.122

Step-by-step explanation:

The expected seeds to be sesame seed bagels is 18

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

Seed bagels = 6

Other bagels = 24

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

Seed bagels : Other bagels = 6 : 24

Simplify

So, we have

Seed bagels : Other bagels = 1 : 4

When there are 90 bagels, we have

Seed bagels = 1/(1 + 4) * 90

Evaluate

Seed bagels = 18

Hence, the number of seed bagels is 18

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Answer:

85 square inches.

Step-by-step explanation:

The area of a triangle can be found by the formula [tex]1/2bh[/tex], assuming b is the base and h is the height.

If b is 17 inches and h is 10 inches:

[tex]1/2(17)(10)[/tex]

[tex]1/2(170)[/tex]

[tex]A = 85[/tex]

Therefore, the area is 85 square inches.

The partial fraction decomposition of x³-x / x⁴+2x²+1 is x³ - x = 1/2/(x² + 1) + (-1/2)/(x² + 1)².

In mathematics, a function is a relationship between two sets of values, called the domain and the range, that assigns to each element of the domain exactly one element of the range. In other words, a function is a rule that takes an input value and produces an output value.

A function can be represented using various notations, such as f(x), g(x), or h(y), where the name of the function (f, g, h) indicates the rule or relationship, and the input variable (x or y) represents the element of the domain. The output variable is denoted by the value of the function, such as f(x) or g(x).

To find the partial fraction decomposition of the given expression, we first factor the denominator:

x⁴ + 2x² + 1 = (x2 + 1)²

Since the degree of the numerator is less than the degree of the denominator, we know that the partial fraction decomposition will have the form:

(x³ - x) / (x⁴ + 2x² + 1) = A/(x² + 1) + B/(x² + 1)²

where A and B are constants to be determined.

To find A, we multiply both sides of the equation by (x² + 1):

x³ - x = A + B(x² + 1)

Setting x = 0, we get:

0 = A + B

To find B, we differentiate both sides of the equation with respect to x:

3x² - 1 = 2B(x² + 1) + 2B(x² + 1)(2x)

Setting x = 0, we get:

-1 = 2B

So, we have:

A = -B = 1/2

Therefore, the partial fraction decomposition of x³-x / x⁴+2x²+1 is:

x³ - x = 1/2/(x² + 1) + (-1/2)/(x² + 1)²

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Using conversions, we can find that the measure of the width of the picnic area in the drawing is 50inches.

Unit conversion is a multi-step procedure that requires multiplying or dividing by a numerical factor, or more specifically, a conversion factor. Furthermore, rounding and choosing the right number of significant digits may be required. Various metrics are measured using various conversion units.

Here in the question,

Actual width of the picnic area = 40yards.

Now, in the drawing Kenny used a scale of 5 inches: 4 yards.

So, in the drawing the width of the picnic area = 5 × 10

= 50 inches.

Therefore, the measure of the width of the picnic area in the drawing is 50inches.

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