Match the vocabulary word with the correct definition.

1. a line segment where two faces meet
edge
2. a three-dimensional figure with one circular base
dimensions
3. to separate something into its basic parts
area
4. units used to measure the volume of a three-dimensional figure
cube
5. a three-dimensional figure with two parallel, congruent, circular bases and a curved surface
decompose
6. a three-dimensional figure made of six congruent squares
composite figure
7. a geometric figure that is made up of two or more basic shapes
base
8. the length of a plane figure; or, a special face of a solid figures
cone
9. the measurement of the space inside a plane figure
cylinder
10. measurements indicating the size and shape of an object, such as length and width
cubic units

Applying the linear pair theorem and the sum of interior angles of hexagon, we have:

Angle 7 = 92°

Angle 1 = 107°

According to the linear pair theorem/postulate, when two angles lie on a straight line, the sum of their measures equals 180 degrees.

Angle 7 lie on a straight line with 88°, therefore, applying the linear pair theorem, we have:

Angle 7 + 88 = 180

Subtract both sides by 88

Angle 7 + 88 - 88 = 180 - 88

Angle 7 = 92°

Also, using the linear pair theorem, we have:

Angle 5 = 180 - 64

Angle 5 = 116°

Angle 3 = 180 - 57

Angle 3 = 123°

Sum of interior angles of hexagon equals 720°, therefore:

Angle 1 + angle 3 + angle 5 + angle 7 + 118 + 164 = 720°

Plug in the known values

Angle 1 + 123 + 116 + 92 + 118 + 164 = 720

Angle 1 + 613 = 720

Subtract both sides by 613

Angle 1 + 613 - 613 = 720 - 613

Angle 1 = 107°

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Answer:

x = 5

Step-by-step explanation:

                       x - 2(x +1) + 3(x -2) + 2(x - 6) = 0

x + (-2)*x  + (-2)*1 + 3*x +3*(-2) + 2*x + 2*(-6) = 0

                            x - 2x -2 + 3x - 6 + 2x - 12 = 0

                          x - 2x + 3x + 2x - 2 - 6 - 12 = 0

Combine like terms. Like terms have same variable with same power.

                                                          4x - 20 = 0

Add 20 to both sides.

                                                                 4x  = 20

Divide both sides by 4

                                                                   x = 20/4

                                                                   x = 5

Answer:

x = 5

Step-by-step explanation:

x  -2(x+1) + 3(x-2) + 2(x-6) =  0

here, we need to distribute the numbers on the outside of the parentheses to the inside numbers.

As you may know, when two numbers are in parentheses, they are to be multiplied--and it is the same idea here.

When we have a number, say 3, multiplied by parentheses, say (x - 2), we multiply all inside numbers by the outside number, which is called distributing.

We know that 3(x) = 3x, and that 3(-2) = -6, so we distribute

3(x  - 2)       to be        3x - 6

let's do that for all of our parentheses:
x  -2(x+1) + 3(x-2) + 2(x-6) =  0

-2( x  + 1 )

-2x   -  2

3(x  - 2)

3x   -  6

2( x  - 6)

2x  - 12

Now, let's rewrite our problem:

x  -2(x+1) + 3(x-2) + 2(x-6) =  0

x     - 2x  - 2    + 3x -6     + 2x - 12    = 0

First, we should combine like terms:

x - 2x  + 3x + 2x          - 2 - 6 - 12    = 0

(x - 2x = -x;  -x + 3x = 2x;  2x + 2x = 4x)

( - 2 - 6 = -8; -8 - 12 = -20

So, we are left with:

4x  -  20 = 0

At this point, we want to get x alone (so that we can find what "x" is)

4x - 20 = 0  

    + 20    + 20       ( add 20 to both sides of the equation to isolate x )  

   4x     =    20

  ÷ 4          ÷ 4           (divide both sides by 4 to find "1"x)

     x  =  5

So, we know that the value of x is 5, or x = 5

hope this helps! let me know if you need clarification on anything :)

Answer:

b = -a

Step-by-step explanation:

Since a and b are equally distant to zero but in opposite directions, a and b are opposites, or additive inverses.

The sum of additive inverses is zero.

a + b = 0

b = -a

The common ratio of the set of data is 0. 1

To determine the common ratio of a set of data, we have to

For the given set of data

0.1,0.01,0.001

Let's divide the second term by the first term

= 0. 01/ 0. 1

= 0. 1

Thus, the common ratio of the set of data is 0. 1

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tan45° = cot45° = 1

---> If tanA + cotA = 2, then A is 45°.

---> tan²A + cot²A = 1² + 1² = 2

The correct answer is 2

From the given graph, we can see by tracing that f(4) is -3.5

The given graph is a graph of a quadratic function with a parabola opening upwards.

According to the question, we are to find the value of y where the value of x is 4. From the given graph, we can see by tracing that f(4) is -3.5

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A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]

B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)

Mid point = (X , Y)

X = (x₁ + x₂) / 2

X = (4 + p) / 2

Y = (y₁ + y₂) / 2

Y = (5 + q) / 2

Thus,

Mid point = (X , Y)

Mid point = [(4 + p) / 2 , (5 + q) / 2]

Mid point = (7, 1) = (X , Y)

X = (4 + p) / 2

7 = (4 + p) / 2

Cross multiply

7 × 2 = 4 + p

14 = 4 + p

Collect like terms

p = 14 - 4

p = 10

Y = (5 + q) / 2

1 = (5 + q) / 2

Cross multiply

1 × 2 = 5 + q

2 = 5 + q

Collect like terms

q = 2 - 5

q = -3

Coordinates of D = (p, q)

Coordinates of D = (10 , -3)

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The product of two numbers when doubled, the product of these larger numbers is 35,732

let

product of x and y = 8933

x × y = 8933

2x × 2y = 8933

4xy = 4(8933)

4xy = 35,732

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Answer:

[tex]\textsf{1.} \quad C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

2.   [-273.15, ∞)

Step-by-step explanation:

Given:

[tex]C=\dfrac{5}{9}(F-32), \quad \text{where }F \geq -459.67[/tex]

To find the inverse of the given function, make F the subject:

[tex]\begin{aligned}C & =\dfrac{5}{9}(F-32)\\\implies \dfrac{9}{5}C & =F-32\\\implies F & = \dfrac{9}{5}C+32 \end{aligned}[/tex]

[tex]\textsf{Replace the } F \textsf{ with }C^{-1}(F)\textsf{ and the }C \textsf{ with } F:[/tex] :

[tex]\implies C^{-1}(F)=\dfrac{9}{5}F+32[/tex]

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

The given domain of the function C(F) is F ≥ -459.67

Therefore, the minimum value of the function is:

[tex]\implies C(-459.67)=\dffrac{5}{9}(-459.67-32)=-273.15[/tex]

This means the range of the function C(F) is C(F) ≥ -273.15

The domain of the inverse function is the range of the function.

Therefore, the domain of the inverse function in interval notation is:  [-273.15, ∞)

Answer: -273.15

Step-by-step explanation:

[tex]db {}^{2} - ab {}^{2} = ab {}^{2} - ae {}^{2} \\ db {}^{2} = 2ab {}^{2} - ae {}^{2} \\ (ac + bc) {}^{2} = 2ab {}^{2} - ae {}^{2} \\ ac {}^{2} + bc {}^{2} + 2ac.bc = 2ab {}^{2} - ae {}^{2} \\ 2ac.bc = ab {}^{2} - ae {}^{2} [/tex]

[tex]2ac.bc = ab {}^{2} - (ac {}^{} - ce) {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} + 2ac.ce - ce {}^{2} \\ 2ac.bc = ab {}^{2} - ac {}^{2} - cb {}^{2} + 2ac.ce \\ but \: ab {}^{2} - ac {}^{2} - cb {}^{2} = 0 \\ 2ac.bc = 2ac.ce \\ bc = ce \\ which \: is \: true[/tex]

Answer:

3 times larger

Step-by-step explanation:

Front tire circumference = pi *d

rear tire is 3 times this   = pi 3 d

   so rear tire has radius 3x that of the front tire

Answer:

A

Step-by-step explanation:

As angles in a triangle add to 180 degrees, angle C measures 35 degrees.

Therefore, the answer is A, since thr triangles will be similar by AA.

The total cost to fill Kenny's entire attic given the cost per cubic yards is $904.50; option A

[tex]V = 1/4h \sqrt{ { - a}^{4} + 2 {ab}^{2} } + 2 {ac}^{2} - {b}^{4} + 2 {bc}^{2} - {c}^{4} [/tex]

= 1/4×9 √-4⁴ + 2(4×5)² + 2(4×3)² - 5⁴ + 2(5×3)² - 3⁴

= 9/4√256 + 2(20)² + 2(12)² - 3125 + 2(15)²- 81

= 9/4√256 + 2(400) + 3(144) - 3125 + 2(225) - 81

= 9/4√256 + 800 + 432 - 3125 + 450 - 81

= 9/4√-1268

= 54 cubic yard

Total cost to fill Kenny's entire attic = 54 × $16.75

= $904.50

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The expected value of a roll of this weighted die is; 13/3 or 4.33

We are given that;

A $6 sided die is weighted.

Probability of any number being rolled is proportional to the value of the roll.

Probability of a $2 being rolled is twice that of a $1 being rolled.

Thus, the expected Value is;

E(x) =  (1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6)/(1 + 2 + 3 + 4 + 5 + 6)

E(x) = 13/3 = 4.33

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Step-by-step explanation:

The complete table is

                Dog         Not Dog         Total

Cat            31              10                     41

Not cat     24              7                       31

Total         55              17                      72

Given a venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet as shown in figure which is attached below.

In the figure cat and dog are overlapping which means 31 people like both.

The people that like only dog but not cat are 24 and the people that like only car but not dog is 10.

The people that like not cat not dog is 31-24=7.

The total people that like cats are 31+10=41 and the total people that dont like cat is 24+7=31

The total people that like dogs are 31+24=55 and the people that didn't like dogs are 31+10-24=17 and the total people that like both dog and not dog and also like cat and not cat is 55+17=41+31=72.

Hence, the complete table is shown in attached figure for the given venn diagram.

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Answer:

[tex]y=0.5x-10.5[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is 0.5.

Substituting into point-slope form and converting to slope-intercept form,

[tex]y+6=0.5(x-9) \\ \\ y+6=0.5x-4.5 \\ \\ y=0.5x-10.5[/tex]

The probability that it willtake less than 34 minutes to complete the test is 0.1056

Given mean of 44 minutes and standard deviation of 8 minutes.

We have to find the probability that it will take less than 34 minutes to complete the test.

The probability lies between 0 and 1. The formula to calculate probability is number of items divided by total items but it can also be found through z test calculations.

We are using z test to find the probability.

Z=X-μ/σ

Where μ is sample mean and

σ= standard deviation

Z is z value

First we will find the p value from 34 to 44.

Z=34-44/8

=-10/8

=-1.25

P value for X<34=P(Z<-1.25)

=0.5-0.3944

=0.1056.

Hence the probability that it will take less than 34 minutes is 0.1056.

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(a) The sample mean for:

Sample 1 is 3.4, Sample 2 is 3.4, Sample 3 is 3.6, and Sample 4 is 3.8.

(b) The range of the sample means is 0.4.

(c) The true statement from the given statements are:

The sample mean, [tex]\bar{x}[/tex], is calculated using the formula, [tex]\bar{x} = \frac{\sum x}{N}[/tex], where N is the sample size.

The range of a data is the difference between the greatest data point and the smallest data point.

(a) Thus, the sample mean for:-

Sample 1:

= (3 + 2 + 6 + 4 + 2)/5 = 17/5 = 3.4.

Sample 2:

= (2 + 2 + 3 + 7 + 3)/5 = 17/5 = 3.4.

Sample 3:

= (6 + 4 + 2 + 2 + 4)/5 = 18/5 = 3.6.

Sample 4:

= (5 + 3 + 2 + 5 + 4)/5 = 19/5 = 3.8.

(b) The range of the sample means is 3.8 - 3.4 = 0.4.

(c) The true statement from the given statements are:

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Answer:

[tex]\huge\boxed{\sf x = 55\°}[/tex]

Step-by-step explanation:

Given that,

x° + 35° = 90° (complementary angles)

Subtract 35 to  both sides

x = 90 - 35

x = 55°

[tex]\rule[225]{225}{2}[/tex]

(C) 3,920 people would likely donate.

What is the percentage?

To find about how many people would likely donate:

First, find 80 is what percent of 200.

∴  [tex]\frac{80}{200} * 100 = 40%[/tex]

So, 80 is 40% of 200.

Centreville population is 9,800.

Now, take out 40% of 9,800.

[tex]\frac{x}{9,800} *100 = 40\\\frac{x}{98} =40\\98*40 = 3,920[/tex]

Therefore, (C) 3,920 people would likely donate.

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Using the normal distribution, the probability that the sample proportion will be less than 0.1768 is of 0.9222 = 92.22%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the proportion and the sample size are given by:

p = 0.12, n = 66.

Hence the mean and the standard error are:

The probability that the sample proportion will be less than 0.1768 is the p-value of Z when X = 0.1768, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.1768 - 0.12}{0.04}[/tex]

Z = 1.42

Z = 1.42 has a p-value of 0.9222.

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The skydiver is falling at a speed of 212 miles per hour.

The speed of the skydiver is 212 mph.

What are Speed and Velocity?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, whereas velocity is a vector, speed is a scalar quantity.

Given:

If a skydiver jumps out of a plane and plummets to the ground while falling at 212 mph.

To Find:

Speed and acceleration of the skydiver.

Velocity is the speed with a direction, whereas speed is only a number with a speed unit at the end.

While velocity refers to the speed and direction of an object's movement, speed refers to the time rate at which an object moves along a path.

212 miles per hour is the descending velocity of the skydiver.

At 212 miles per hour, the skydiver is moving.

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Y= 75.

Lets try to solve it,

When positive integer x is divided by positive integer y, the remainder is 9

=> x=qy+9;

=> x/y=96.12

=>x=96y+0.12y (so q above equals to 96);

=>0.12y=9

=> y=75.

Hence the value of y would be 75.

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Answer:

A.

Step-by-step explanation:

36/12 = 3

3*2 = 6 cm

48/12 = 4

4*2 = 8 cm

Answer: 22

Step-by-step explanation:

The function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

In this problem we have two functions related to each other because of the existence of rigid transformations. Rigid transformations are transformations applied to geometric loci such that Euclidean distance is conserved at every point of the geometric locus.

Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of horizontal translation 4 units in the + x direction:

f'(x) = - 2 · cos (x - 1 + 4) + 3

f'(x) = - 2 · cos (x + 3) + 3     (1)

Now we apply a reflection over the x-axis:

g(x) = - [- 2 · cos (x + 3) + 3]

g(x) = 2 · cos (x + 3) - 3

Therefore, the function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

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Since we are dealing with a proportion, it is determined by using the z-distribution that there is insufficient evidence to draw the conclusion that the proportion of all kochia plants that are resistant to glyphosate has increased because the test statistic is less than the critical value for the right-tailed test.

In this problem, we consider that:

[tex]$H_{0}: p_{2}-p_{1}=0$[/tex]

[tex]$H_{1}: p_{2}-p_{1} \neq 0$[/tex]

The proportions and standard errors are given by:

[tex]p_{1}=0.197, s_{1}=\sqrt{\frac{0.197(0.803)}{61}}=0.0509\\p_{2}=0.385, s_{2}=\sqrt{\frac{0.385(0.615)}{52}}=0.0675[/tex]

Hence, the distribution has mean and standard error given by:

[tex]\bar{p}=p_{2}-p_{1}=0.0675-0.0509=0.0166\\s=\sqrt{s_{1}^{2}+s_{2}^{2}}=\sqrt{0.0509^{2}+0.0675^{2}}=0.0845[/tex]

It is given by:

[tex]$z=\frac{\bar{p}-p}{s}$[/tex]

In which p = 0 is the value tested at the null hypothesis, hence:

[tex]z=\frac{0.0166}{0.0845}\\$z=0.2$[/tex]

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Because It is quicker and fast.

Sampling:

Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.

Sampling is the selection of a subset of the population of interest in a research study. In the vast majority of research endeavors, the participation of an entire population of interest is not possible, so a smaller group is relied upon for data collection.

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