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Answer:

The total volume of the solid is 1.67 cubic units.

Step-by-step explanation:

Each pyramid with a height of 2 units and a rectangular base with dimensions of 5 units × 0.25 units.

1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2= 0.833

Therefore, the volume of each pyramid will be

= cubic units.

So, the total volume of the solid is (2 × 0.833) = 1.67 cubic units. (Answer)

Hope it helped ya!

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Tysmm

The total volume of the solid is 1.67 unit³.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given:

Each pyramid has a height of 2 units.

and the rectangular base with dimensions of 5 units × 0.25 units.

So, the Volume of each Pyramid is

= 1/3 x (area of base) x height

= 1/3 x (5 x 0.25) x 2

= 0.833

and, the total volume of the solid

= (2 × 0.833)

= 1.67 cubic units.

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Answer:99

Step-by-step explanation:(11×9)×1=99

Answer:

Step-by-step explanation:

(a x b) x c

a = 11, b = 9, and c = 1

In order to solve substitute the values of a , b and c into the above expression

That's

( 11 × 9) × 1

Solve the terms in the bracket first

99 × 1

We have the final answer as

Hope this helps you

Answer:

no solution

Step-by-step explanation:

1/3(12-6x)=4-2x

4-1.3x=4-2x

4=4-0.7x

0=0.7x

ns

Hi there! Hopefully this helps!

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It decreased by 30 cents per week.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The average rate of change is calculated as:

the ratio of the sum of the change in the three weeks divided by the number of weeks. (The number of weeks being 3)

 Rate of change = [tex]\frac{-60 -10 -20}{3}[/tex].

(-60 + -10 + -20 = -90). So, to simplify it:

[tex]\frac{-90}{3}[/tex] = -30

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Incase you are confused:

Since the average rate of change is negative, this means that the stock price has decreased.

Answer:

A=80 , B=65, C=35

Step-by-step explanation:

A-B=15 ⇒A=B+15

B-C=30⇒-C=30-B ⇒C=B-30

the sum of angle of a triangle = 180

A+B+C=180 ( substitute A and C)

B+15+B+B-30=180

3B-15=180

3B=180+15

B=195/3=65

C=B-30 ⇒ C=65-30=35

A=B+15=65+15=80

check : A+B+C=180

             80+65+35=180 ( correct)

Answer:

A, C

Step-by-step explanation:

Only B is containing a variable .

The  -5 is not variable.

We have given that,

A.3x2

B. y

A

C. -5

In the expression 3x^2 + y -5

We have to determine which of the following terms does not have a variable.

variable, In algebra, a symbol stands in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

Only C contains a variable.

The  -5 is not variable.

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Answer:

Step-by-step explanation:

For the m it would just be -3 because the equation for slope intercept form is y=mx+b

Answer:

Mean

Step-by-step explanation:

mean is the average of numbers put together and divided by the total amount of numbers, when finding the average annual income using the mean would be most effective

Answer:

The Answer would be ∠W ≅ ∠C

Step-by-step explanation:

Only one that is congruent

The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

A triangle is a three-sided polygon with three edges and three vertices in geometry.

Given that the triangle ∆MTW is congruent to the triangle ∆CAD.

So, we have

∠MTW ≅ ∠CAD

∠WMT ≅ ∠DCA

∠TWM ≅ ∠ADC

If two triangles are equivalent, the ratio of matching sides will stay constant.

The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.

Therefore, at that point, the right choice is B.

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Answer:

C

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The lower quartile range is shown by the bottom of the box which is at 10.

The median is shown in the middle line, which is closer to 18 than 18.5.

The upper quartile range in the end of the box, which is at 22!

(You can also look at the picture attached if that helps.)

Answer:

Area of the shaded region= 82.2 cm²

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

Step-by-step explanation:

1)First convert mixed fraction to improper fraction and them prime factorize

[tex]6\frac{1}{4} = \frac{25}{4}\\[/tex]

[tex]\sqrt{\frac{25}{4}}= \sqrt{\frac{5*5}{2*2}}= \frac{5}{2} = 2 \frac{1}{2} \\\\[/tex]

2)

[tex](2 \frac{1}{2}- 1 \frac{1}{2})*1 \frac{1}{7}=( \frac{5}{2}- \frac{3}{2})* \frac{8}{7}\\\\\\= \frac{2}{2}* \frac{8}{7}\\\\=1* \frac{8}{7}= \frac{8}{7}\\\\\\=1 \frac{1}{7}[/tex]

3) 0.00706 = 7.06 * [tex]10^{-3}[/tex]

4) 144 = 12 * 12

12 = 6*2

6 = 2*3

Prime factorization of 144 = 2 * 3 * 2 * 2 * 3 *2

                                          = 2⁴ * 3²

5) To find LCM, prime factorize 96 & 144

96 = 2 * 2 * 2 * 2 * 2 * 3 = 2⁵ * 3

144 = 2⁴ * 3²

LCM = 2⁵ * 3² = 32 * 9 = 288

6) HCF

105 = 7 * 5 * 3

135 = 5 * 3* 3 * 3

180 = 5 * 3 * 3 * 2 * 2

HCF = 5 * 3 = 15

7) 24 = 3 * 2 * 2 * 2 = 3 * 2³

   36 = 3 * 3 * 2 * 2 = 3² * 2²

   40 = 5 * 2 * 2 * 2 = 5 * 2³

LCM = 5 * 2³ * 3² = 5 * 8 * 9  = 360

HCF = 2² = 4

Difference = 360 - 4 = 356

8) Multiply each digit of the binary number by the corresponding power of 2, solve the powers and add them all

1111 = 1 *2³ + 1*2² + 1*2¹ + 1*2° = 8 + 4 + 2 + 1 = 15

Ans: 15

9) 36₇ = 102₅

10) 6.9163 = 6.916

I knew only this much

hope it's helpful

:)

Answer:

The two integers are greater than or equal to 17 and 19

Step-by-step explanation:

Consecutive odd integers means 1, 3, 5, 7, 9 and so on

That means there is a always a gap of 2 in between each of them. Knowing this, we can set up an equation. Let x represent the first of the consecutive integers.

x+(x+2)=36

x+2 represents the second consecutive interger

x+x=34

2x=34

x=17

The two integers are 17 and 19

Answer:

1. Data point A

4. Data point D

Step-by-step explanation:

In a scatter plot, the closer the clustered data points are close to the best line of fit, the greater the correlation that would exist between the two variables.

If we are to draw a best line of fit in the scatter plot that is shown above, the closest data points amongst data points A, B, C, D, and E, that would be close to the best line of fit are data points A and D.

Therefore, removing data point A and point D would cause the correlation to decrease the most.

Answer:

5.6803 has five significant figures.

0.00047 has two significant figures.

0.240 has three significant figures.

Significant figures are numbers that are necessary to express a true value.

Place the values in scientific notation.

[tex]5.6803 * 10^{0} = 5.6803\\\\4.7 * 10^{-4} = 0.00047\\\\2.4 * 10^{-1}=0.240[/tex]

5.6803

The zero that is within 5.6803 is "trapped," meaning it is in between two nonzero digits. Therefore, all five digits are significant figures.

This answer is also already in scientific notation because 5.6803 satisfies the inequality [tex]1 < x < 10[/tex], which decides if a number is correctly written in scientific notation or not.

0.00047

The zeroes that precede the 4 and the 7 are not significant because they are dropped in scientific notation and are not trapped by other nonzero digits. Therefore, only two digits of this value are significant.

0.240

Since the zero at the end of 0.240 is a trailing zero, it is significant along with the 2 and the 4. The zero that precedes these digits and the decimal point is not significant. Therefore, only three digits of this value are significant.

Therefore:

5.6803 has five significant figures.

0.00047 has two significant figures.

0.240 has three significant figures.

Answer:

D) BAC is the correct answer as A is at the middle.

All of the options describe an angle with a vertex at A.

In geometry, a vertex is a point where two or more lines, curves, or edges meet to form an angle or a corner.

It is the common endpoint of two or more rays, line segments, or sides of a polygon.

We have,

All of the options describe an angle with a vertex at A.

In each option, A is the vertex of the angle.

The letters that come before and after A indicate the other two points that form the angle. So:

∠ABC is an angle with vertex A and points B and C on either side.

∠CAB is an angle with vertex A and points C and B on either side. (Note that the order of the letters is reversed from option A.)

∠ACB is an angle with vertex A and points C and B on either side. (Note that the order of the letters is reversed from option B.)

∠BAC is an angle with vertex A and points B and C on either side. (Note that the letters are in a different order than option A.)

Thus,

All of the options describe an angle with a vertex at A.

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Answer:

Approximately 439.6 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cone is the following:

[tex]A=\pi r^2+\pi r l[/tex]

Where, r is the radius and l is the slant height.

The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:

[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]

Answer:

292.77

Step-by-step explanation:

πr(r+[tex]\sqrt{h2+r2}[/tex])

13 x 2 = 26

7 x 2 = 14

26 + 14 = 40

[tex]\sqrt{40}[/tex] = 6.32

7 + 6.32 = 13.32

3.14 x 7 = 21.98

21.98 x 13.32 =

292.77

Answer:

6

Step-by-step explanation:

Doing the fourth root of something is the equivalent of doing said number to the power of 1/4. So in this case I will convert the fourth root into an exponent and simplify:

6^(4*1/4) = 6^1 = 6

Hope this helps!

Answer:

The probability that 100 or fewer will have 3 ​girls is 0.00734.

Step-by-step explanation:

The complete question is:

In a family with ​3 children, the probability that all the children are girls is approximately 0.125. In a random sample of 1000 families with ​3 children, what is the approximate probability that 100 or fewer will have 3 ​girls? Approximate a binomial distribution with a normal distribution.

Solution:

Let X represent the number of families who has 3 girls.

The random variable X follows a Binomial distribution with parameters n = 1000 and p = 0.125.

But the sample selected is too large.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

1. np ≥ 10

2. n(1 - p) ≥ 10

Check the conditions as follows:

 [tex]np=1000\times 0.125=125>10\\\\n(1-p)=1000\times (1-0.125)=875>10[/tex]

Thus, a Normal approximation to binomial can be applied.

So,  [tex]X\sim N(\mu=np,\sigma^{2}=np(1-p))[/tex]

The mean and standard deviation are:

[tex]\mu=np=1000\times 0.125=125\\\\\sigma=\sqrt{np(1-p)}=\sqrt{1000\times 0.125\times (1-0.125)}=10.46[/tex]

Compute the probability that 100 or fewer will have 3 ​girls as follows:

Apply Continuity correction:

[tex]P(X\leq 100)=P(X<100-0.50)[/tex]

                  [tex]=P(X<99.50)\\\\=P(\frac{X-\mu}{\sigma}<\frac{99.5-125}{10.46})\\\\=P(Z<-2.44)\\\\=0.00734[/tex]

*Use a z-table.

Thus, the probability that 100 or fewer will have 3 ​girls is 0.00734.

Part (a)

The length is supposed to be 22.2 cm, but it could be 0.3 cm less

So 22.2 - 0.3 = 21.9 cm is the smallest value for the length. This is the lower bound of the length.

The upper bound is 22.2 + 0.3 = 22.5 cm as it is the largest the length can get.

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

Use this for the width as well

The width is supposed to be 12 cm, but it could be as small as 12-0.3 = 11.7 cm and as large as 12+0.3 = 12.3 cm

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

============================================

Part (b)

Use the smallest length and width to get the smallest possible area

smallest area = (smallest width)*(smallest length) = 11.7*21.9 = 256.23

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

Repeat the same idea but for the largest length and width to get the largest possible area

largest area = (largest width)*(largest length) = 12.3*22.5 = 276.75

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Answer:

[tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex]

Step-by-step explanation:

[tex]\frac{4x}{(x-3)}+\frac{6}{(x+2)}[/tex]

= [tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]

Now we have done the denominators of each term of the expression equal.

Further we add the terms,

[tex]\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}[/tex]

= [tex]\frac{4x(x+2)+6(x-3)}{(x-3)(x+2)}[/tex]

= [tex]\frac{4x^{2}+8x+6x-18}{(x-3)(x+2)}[/tex]

= [tex]\frac{4x^{2}+14x-18}{(x-3)(x-2)}[/tex]

Now factorize the numerator of the fraction.

4x² + 14x - 18 = 2(2x² + 7x - 9)

                     = 2(2x² + 9x - 2x - 9)

                     = 2[x(2x + 9) - 1(2x + 9)]

                     = 2(x - 1)(2x + 9)

Therefore, [tex]\frac{2(x-1)(2x+9)}{(x-3)(x-2)}[/tex] will be the answer.

Answer:

Hey there!

The overlapping part is the product.

Thus, the product is 1/8.

Hope this helps :)

Answer:

140°

Step-by-step explanation:

total angle of a hexagon is 720. We know already 510°. That leaves 210°. The ratio between the two angles is 2:1, therefore angle CDE is 140° and angle DEF is 70 °

Answer:

140°

Step-by-step explanation:

We know that all of these angles here are part of a hexagon, meaning that their angle measures will all add up to 720°.

We can use what we already know and find what CDE and DEF will add up to.

[tex]145+90+160+115=510\\720-510=210[/tex]

Now, assuming x is the measure of DEF, we can create an equation for this.

[tex]x + 2x = 210\\3x = 210\\x = 70[/tex]

This is the measure of DEF, but it asks for CDE, which is twice the size of DEF. So

[tex]70\cdot2=140[/tex]

We can double check this is right by adding up all the measures.

[tex]145+90+160+115+140+70=720[/tex]

Hope this helped!

Answer:

see explanation

Step-by-step explanation:

tan x = -1

[tex]x = tan^{-1}(-1)[/tex]

x = -45

tan x = 5

[tex]x = tan^{-1}(5)[/tex]

x = 78.69

Answer:

See below.

Step-by-step explanation:

So we want to find the solutions to the two equations:

[tex]\tan(x)=-1 \text{ and } \tan(x)=5[/tex]

I)

[tex]\tan(x)=-1\\x=\tan^{-1}(-1)[/tex]

Recall the unit circle. First, note that the number inside tangent is negative. Because of this, we can be certain that the x (in radians) must be in Quadrant II and/or IV (This is because of All Students Take Calculus, where All is positive in QI, only Sine is positive in Q2, only Tangent is positive in Q3, and only Cosine is positive in QIV. Tangent is negative so the only possible choice are QII and QIV).

From the unit circle, we can see that x=3π/4 is a possible candidate since tan(3π/4)=-1.

Since tangent repeats every π, 7π/4 must also be an answer (because 3π/4 + π = 7π/4). And, as expected, 7π/4 is indeed in QIV.

Therefore, for the first equation, the solutions are:

[tex]x=3\pi/4 \text{ and } 7\pi/4[/tex]

II)

For the second equation, there is no exact value for which tangent of an angle would be equal to 5. Thus, we need to approximate.

So:

[tex]\tan(x)=5\\x=\tan^{-1}(5)\\x=\tan^{-1}(5) \text{ and } \tan^{-1}(5)+\pi[/tex]

We got the second answer because, like previously, tangent repeats every π, so we only need to add π to get the second answer.

In approximations, this is:

[tex]x\approx1.3734 \text{ and } x\approx4.5150[/tex]

Note: All the answers are in radians.

Answer:

Total area = 29.8 sq. units

Step-by-step explanation:

area of each triangle =  sqrt(s * (s-a) * (s-b) * (s-c))

to get the value of s, use the semi-perimeter = s = perimeter / 2

Total area = area of triangle ABD + area of triangle ACD

semi-perimeter of ABD = (3.48 + 8.66 + 8.6) / 2 = 10.37

semi-perimeter of ABD = (3.54 + 8.84 + 8.6) / 2 = 10.49

area of triangle ABD = sqrt(10.37 * (10.37-3.48) * (10.37-8.66) * (10.37-8.6))

area of triangle ABD = 14.7 sq. units

area of triangle ACD = sqrt(10.49 * (10.49-3.54) * (10.49-8.84) * (10.49-8.6))

area of triangle ACD = 15.08

Total area = 14.7 + 15.1

Total area = 29.8 sq. units

Answer:

x=4

Step-by-step explanation:

it's a identity function because it is in the form of f(x)= x ,so the value of x is 4.

Answer:

  $887.50

Step-by-step explanation:

Her gross pay is the sum of the pay amounts for each of the hour amounts:

  pay = 40(12.50) +18(12.50)(1.5) +2(12.50)(2)

  = (12.50)(40 +18(1.5) +2(2)) = 12.50(40 +27 +4) = 12.50(71)

  pay = 887.50

Barbara's gross pay for the week was $887.50.

Answer:

[tex] d = 55h [/tex]

Step-by-step explanation:

We are given that Chantal drives at a constant speed of 55 miles per hour.

If, d represents the total distance in miles, and

h represents number of hours, the following equation can be used to express the given situation:

[tex] d = 55h [/tex]

For every hour, a distance of 55 miles is covered.

Thus, if h = 1, [tex] d = 55(1) = 55 miles [/tex]

If h = 2, [tex] d = 55(2) = 110 miles [/tex].

Therefore, [tex] d = 55h [/tex] , is an ideal equation that represents the situation given in the question above.

To find the area of a triangular prism you have to do A 1/2 bh or A bh/2 which means you have to multiply those two fractions and reduce them

Answer:

Find the area of the 2 triangle faces first and then find the area of the 3 rectangle faces and add them together to get [tex]159cm^{2}\\[/tex]

Step 1: Find the surface area of the 2 triangles

[tex]\frac{(6)(5.5)}{2}[/tex] x2 = [tex]33cm^2\\[/tex]

Step 2: Find the surface area of the 3 rectangles

(6x7) x 3 = [tex]126cm^2[/tex]

Step 3: Add the 2 surface areas together

[tex]33cm^2\\[/tex] + [tex]126cm^2[/tex] = [tex]159cm^2[/tex]

Therefore the surface area of the prism is [tex]159cm^{2}[/tex]

Answer:

The distance of  Musah's final point from the center in the west direction is   60.355 steps

The distance of  Musah's final point from the center in the north direction is   85.355 steps

Step-by-step explanation:

Given that :

Musah stands at the center of a rectangular field.

He takes 50 steps north, then 25 steps West and finally 50 on a bearing of 315°.

The sketch for Musah's movement is seen in the attached file below.

How far west is Musah's final point from the centre?

In order to determine how far west  is Musah's,

Let d be the distance of how far west;

Then d = BC + CD cos θ

In the North West direction,

cos θ = cos 45°

d = 25 + 50( cos 45°)

d = 25 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex]  )

d = 25 + 50( 0.7071)

d =25 + 35.355

d = 60.355 steps

How far north is Musah's final point from the center?

Let d₁ be the distance of how far North;

Then d₁ = AB + CD sin  θ

d₁ = 50 + 50  sin  45°

d₁ = 50 + 50([tex]\dfrac{1}{\sqrt{2}}[/tex]  )

d₁ = 50 + 50( 0.7071)

d₁ = 50 + 35.355

d₁ = 85.355  steps