8
Half a number increased by 10 is
equal to 35 less than twice the
number. What is the number?
​

Answer:

The height of the water is [tex]60.5\ ft[/tex]

Step-by-step explanation:

step 1

Find the volume of the tank

The volume of the inverted right circular cone is equal to

[tex]V=\frac{1}{3}\pi R^{2} H[/tex]

we have

[tex]R=16\ ft[/tex]

[tex]H=96\ ft[/tex]

substitute

[tex]V=\frac{1}{3}\pi (16)^{2} (96)[/tex]

[tex]V=8,192\pi\ ft^{3}[/tex]

step 2

Find the 25% of the tank’s capacity  

[tex]V=(0.25)*8,192\pi=2,048\pi\ ft^{3}[/tex]

step 3

Find the height, of the water in the tank  

Let

h ----> the height of the water  

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional

[tex]\frac{R}{H}=\frac{r}{h}[/tex]

substitute

[tex]\frac{16}{96}=\frac{r}{h}\\ \\r= \frac{h}{6}[/tex]

where

r is the radius of the smaller cone of the figure

h is the height of the smaller cone of the figure

R is the radius of the circular base of tank

H is the height of the tank

we  have

[tex]V=2,048\pi\ ft^{3}[/tex] -----> volume of the smaller cone

substitute

[tex]2,048\pi=\frac{1}{3}\pi (\frac{h}{6})^{2}h[/tex]

Simplify

[tex]221,184=h^{3}[/tex]

[tex]h=60.5\ ft[/tex]

Answer:

Polygons are 2 dimensional figures and have NO volume.

Maybe you are thinking of polyhedrons?

If 2 polyhedrons have the same volume, they are probably NOT congruent.

Step-by-step explanation:

Final answer:

Polygons are considered congruent if they can be superimposed with matching corresponding segments and angles. Polygons with equal area or equal content are not necessarily congruent; they may have the same size but their shapes can differ.

Explanation:

When referring to two polygons, the term "congruent" is used to describe figures where not only the corresponding angles are equal but also the lengths of corresponding sides are equal. In contrast, polygons having the same volume, which applies to three-dimensional solids or having the same area, which applies to two-dimensional figures, do not necessarily need to be congruent. According to our established theorems in geometry, two polygons are considered congruent if they can be superimposed on one another such that every corresponding segment and angle matches. In the case of polygons, this means that the lengths of sides and angles are exactly the same in both figures.

The concept of equal area differs from congruence. Polygons of equal area have the same total size in terms of square units, but their shapes can be vastly different. Therefore, polygons with equal area or equal content aren't necessarily congruent because congruence requires the polygons to have identical size and shape, with all corresponding sides and angles being equal. Equal content refers to the possibility of adding other polygons of equal area to two non-congruent polygons to achieve two resulting polygons with equal area. It's important to note that while congruent figures will always have equal content and area, figures with equal content and area may not be congruent.

Answer:

3 3/7 hours.

Step-by-step explanation:

We work in  rates / hour:

Anita  does 1/8 of the pool in 1 hour and Chao does 1/6 in an hour.

Let x be the time they would clean the pool working together,  then we have:

1/8 + 1/6 = 1/x

3/24 + 4/24 = 1/x

7/24 = 1/x

7x= 24

x = 24/7 hours.

It will take 24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds) hours to clean a typical pool Anita and Chao working together.

The typical setup for these work problems is

                         [tex]\frac{t}{a}+\frac{t}{b} =1[/tex]

Here, a and b are how long they can do it by themselves, and t is how long they work together.

                      ⇒[tex]\frac{t}{8}+\frac{t}{6} =1[/tex]

Now, we will do LCM of 8 and 6 and we get 24;

                     ⇒[tex]\frac{3t+4t}{24} =1[/tex]

                     ⇒[tex]\frac{7t}{24}=1[/tex]

Now, we will multiply 24 on both sides, and we get;

                    ⇒[tex]7t=24[/tex]

Now, we will divide by 7 on both sides, we get:

                   ⇒[tex]t=\frac{24}7}[/tex]

Hence, the answer is [tex]\frac{24}7}[/tex] hours.

x=24/7 ≈ 3.43     (3 hours,  25 minutes, 43 seconds)

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.

The lowest common multiple of 3 and 8? Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24... Multiples of 8 are 8, 16, 24, 32, 40... So the lowest common multiple of 3 and 8 is 24.

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Hi I am gonna I wanna go to see the

Answer:

C.14

Step-by-step explanation:

Answer:

B. 2

Step-by-step explanation:

To find the slope of the line, use the slope formula. Use the coordinates of the two red dots to find the slope of the line.

slope = y2-y1 / x2-x1

         = 2-(-2) / 3-1

         = 4/2 = 2

Hope this helps!

The answers here is

B. 2

Answer:

x = sugar cookies dough

y = chocolate chips cookies

13x + 6y = 252

8x + 12y = 288

x = 12, y = 16

Step-by-step explanation:

x = sugar cookies dough

y = chocolate chips cookies

Equation

13x + 6y = 252 ------------ Equation 1

8x + 12y = 288 ------------ Equation 2

Equation 1 x 2

26x + 12y = 504 ------------ Equation 3

Equation 3 - Equation 2

18x = 216

x = 12

Sub x = 12 into Equation 1

13 (12) + 6y = 252

156 + 6y = 252

6y = 96

y = 16

The cost of one package of sugar cookie dough is $12 and one package of chocolate chip cookie dough is $16 .

Equation is what relates an unknown variables with other known variables by an equal sign.

It is asked to find

cost of each of one package of sugar cookie dough

one package of chocolate chip cookie dough.

Let the price of sugar cookies dough packet be $x

Let the price of  chocolate chips cookies packet be $y

Then from the given data

13x + 6y = 252

8x + 12y = 288

On solving the equations by elimination method

18x = 216

x = 12

On substituting x = 12

13 (12) + 6y = 252

156 + 6y = 252

6y = 96

y = 16

Therefore the cost of one package of sugar cookie dough is $12 and one package of chocolate chip cookie dough is $16 .

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Answer: 0.5

Step-by-step explanation:

1-5 is half

and 6-10 is half

The probability that the number she chooses is greater than 5 is 5/10 or 1/2.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Elena randomly chooses a number from 1 to 10.

We have to find the probability that the chosen number is greater than 5.

Total amount of numbers from 1 to 10 = 10

The numbers greater than 5 from 1 to 10 are 6, 7, 8, 9 and 10.

Amount of numbers greater than 5 = 5

Probability = Number of desired outcomes / Total number of outcomes

                  = 5 / 10

                  = 1/2

Hence the required probability is 1/2.

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Answer:

I would say C Sets 2 and 3 contain outliers.

Step-by-step explanation:

Set 2 has an outlier of 90, and set 3 contains an outlier of 40. 40 is not as much of an outlier as 90, so I'm not absolutely sure.

Answer:

-Sets 2 and 3 contain outliers.

Step-by-step explanation:

Mean is the average value of the set. Mean deviation is the difference of the values of the set when compared to the mean.

In set 1 the values are between 50 and 60. This means that the mean will also be between 50 and 60.

In set 2 there is one outlier that is 38. So, the range of the values are between 38 and 90. More values are between 30 and 40 so the mean will be in this range. So (90 - the mean in the range between 30 and 40) will be a large number.

The same goes for set 3.

let's firstly convert the mixed fractions to improper fractions and then sum them up.

[tex]\bf \stackrel{mixed}{2\frac{2}{8}}\implies \cfrac{2\cdot 8+2}{8}\implies \stackrel{improper}{\cfrac{18}{8}}~\hfill \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{18}{8}+\cfrac{9}{4}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)18+(2)9}{8}}\implies \cfrac{18+18}{8}\implies \cfrac{36}{8}\implies \cfrac{9}{2}\implies 4\frac{1}{2}[/tex]

The answer is 150 degrees.

The sum of angle in a triangle is 180 degrees.. The measure of <1 from thediagram is 150 degrees

The sum of angle in a triangle is 180 degrees. From the given disgaram, the sum of the angles of the right triangle is 180 degrees.

Using the expression to find the measure of the acute angle

90 + 60+x = 180

150 + x = 180

x = 180 - 150

x = 30

Determne the value of <1

<1 + 30 = 180

<1 = 180 - 30

<1 = 150degrees

Hence the measure of <1 from thediagram is 150 degrees

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Answer:

No, the inverse function does not pass the vertical line test.

Step-by-step explanation:

Remember that [tex]h(x)=y[/tex]. To find the inverse of our function we are going to invert x and y and solve for y:

[tex]h(x)=x^2+3[/tex]

[tex]y=x^2+3[/tex]

[tex]x=y^2+3[/tex]

[tex]x-3=y^2[/tex]

[tex]y=\pm\sqrt{x-3}[/tex]

[tex]h^{-1}(x)=\pm\sqrt{x-3}[/tex]

Now we can graph our function an perform the vertical line test (check the attached picture).

Remember that the vertical line test is a visual way of determine if a relation is a function. A relation is a function if and only if it only has one value of y for each value of x. In other words, a relation is a function if a vertical line only intercepts the graph of the function once.

As you can see in the picture, the vertical line x = 15 intercepts the function twice, so the inverse function h(x) is not a function.

We can conclude that the correct answer is: No, the inverse function does not pass the vertical line test.

Answer:

a. No, the inverse function does not pass horizontal line test

Step-by-step explanation:

h(x) = x² + 3

y = x² + 3

y - 3 = x² ⇒  x² = y - 3

[tex]\sqrt{x^{2} } = \sqrt{y-3} \\[/tex][tex]

x =  \sqrt{y - 3} , -\sqrt{y-3}[/tex]

h^{-1} x = \sqrt{x - 3} , -\sqrt{x-3}[/tex]

The function h^{-1} x fails the horizontal line test, it is not a one to one function.

So, option a is correct

Answer:

[tex]6x^{13}y^{17}[/tex]

Step-by-step explanation:

We need to multiply

[tex]3x^8y^9.2x^5y^8[/tex]

We know the exponent rule of multiplication:

[tex]x^a y^b . x^cy^d = x^{a+c}y^{b+d}[/tex]

If the bases are same the powers are added.

So,

[tex]=3*2 *x^8*x^5*y^9*y^8\\=^{8+5}y^{9+8}\\=6x^{13}y^{17}[/tex]

So, the answer is:

[tex]6x^{13}y^{17}[/tex]

Answer: 537-254=283

Hope this helped!

Answer:

The answer is 283.

Step-by-step explanation:

Subtract the total of 537, by the number of people playing instruments, 254.

537 - 254 = 283

283 is the number of people without instruments.

Hope this helps! :)

Log base 3 of 4 + log base 3 of 11= log base 3 of 4•11; Answers is 11

The answer is:

The dimensions of the paper for Gift C, are: 25" x 12"

and its area is:

[tex]GiftCArea=300inch^{2}[/tex]

To solve the problem, we need to calculate the total area of the remaining paper, and then, subtract it from the paper used for the gift A and B.

We know that:

[tex]GiftA=TotalPaperArea*\frac{2}{5}\\\\GiftB=TotalPaperArea*\frac{1}{3}[/tex]

Now, the paper for Gift C will be:

[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]

From the statement we know that the dimenstions of the remaining paper are 25" x 45", so calculating the area we have:

[tex]TotalArea=25inch*45inch=1125inch^{2}[/tex]

Now, calculating the area of the paper for Gift A and B, we have:

[tex]GiftA=1125inch^{2}*\frac{2}{5}=450inch^{2}\\\\GiftB=1125inch^{2}*\frac{1}{3}=375inch^{2}[/tex]

Then, calculating the paper for Gift C, we have:

[tex]GiftCArea=(TotalPaperArea)-(PaperArea*\frac{2}{5}+PaperArea*\frac{1}{3})[/tex]

[tex]GiftCArea=1125inch^{2}-(450inch^{2}+375inch^{2}+)[/tex]

[tex]GiftCArea=1125inch^{2}-825inch^{2}=300inch^{2}[/tex]

[tex]GiftCArea=300inch^{2}[/tex]

Therefore, calculating the dimensions of the paper for Gift C, knowing the height of the paper (25inches), we have::

[tex]GiftCArea=Height*Width\\\\Width=\frac{GiftCArea}{25inches}=\frac{300inches^{2} }{25inches}=12inches[/tex]

Hence, the dimensions of the paper for Gift C, are: 25" x 12".

Have a nice day!

The domain of the given function is:

                  [tex]x\geq 5[/tex] i.e. [5,∞)

Domain of a function--

The domain of a function is the set of all the possible values of x for which the function is defined.

That is it is the collection of all the points except the excluded values of the function.

The function f(x) is a square root function which is given by:

          [tex]f(x)=2\sqrt{x-5}[/tex]

We know that the domain of the function depends on the domain of the square root quantity.

We know that: a square root function is well defined when the quantity under the square root is non-negative

i.e.

[tex]x-5\geq 0\\\\i.e.\\\\x\geq 5[/tex]

2(x-50)

2(x+3)

7(2-x)

Find the greatest common factors and then put them outside the parentheses

Answer:

12 gallons of 20% salt solution

Step-by-step explanation:

Let

x -----> the number of gallons of 20% salt solution

we know that

20%=20/100=0.20

40%=40/100=0.40

25%=25/100=0.25

so

0.20(x)+0.40(4)=0.25(x+4)

Solve for x

0.20x+1.60=0.25x+1

0.25x-0.20x=1.60-1

0.05x=0.60

x=12 gallons

By solving a linear equation, we will see that we must use 12 gallons of 20% salt solution.

If we mix x gallons of 20% salt with 4 gallons of 40% salt, we will have a total mass of (x + 4 gall).

And the concentration on the left side is the known one, and we want the concentration of the mixture to e 25%, so we will have that:

x*0.20 + 4gal*0.40 = (x + 4gal)*0.25

(the percentages must be written in decimal form).

Now we can solve this linear equation for x:

x*0.20 + 4gal*0.40 = (x + 4gal)*0.25

4gal*0.40 = x*0.25 - x*0.20 + 4gal*0.25

4gal*0.40 -  4gal*0.25 =  x*0.25 - x*0.20

4gal*0.15 = x*0.05

(4gal*0.15)/0.05 = x = 12

So you should use 12 gallons of the 20% salt solution.

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Answer:

C) 24

Step-by-step explanation:

1. Since the perimeter of a triangle is the sum of its three sides, you can write the following expression, solve for x and get the value of each side.

[tex]2x+(2x+2)+(2x+4)=24\\2x+2x+2+2x+4=24\\6x+2+4=24\\6x+6=24\\6x=24-6\\6x=18\\x=\frac{18}{6}\\x=3[/tex]

2. So, replacing the value of x, you can calculate the values of each side of the triangle:

First side:

[tex]2x=2(3)=6[/tex]

Second side:

[tex](2x+2)=(2(3)+2)=6+2=8[/tex]

Third side:

[tex](2x+4)=(2(3)+4)=6+4=10[/tex]

As the larger side is the third one, it is the hypotenuse. So, the base and the  height.

3. The formula to find the area of the right triangle is given by the expression:

[tex]A=\frac{b*h}{2}[/tex]

Where b is the base and h is the height of the triangle, so replacing the values we found, we have the following:

[tex]A=\frac{8*6}{2}[/tex]

[tex]A=\frac{48}{2}[/tex]

[tex]A=24[/tex]

Therefore the answer is C) 24

Final answer:

Bred can paint the wall in 6 different ways using 8 horizontal stripes, considering a maximum of 2 colors out of blue, red, and white with enough paint for 5 stripes of each color.

Explanation:

The question at hand involves combinatorics, which is a branch of mathematics dealing with combinations and permutations. Bred can paint a wall with 8 horizontal stripes using at most 2 colors from the options of blue, red, and white, with enough paint for 5 stripes of each color. Since he is using at most 2 colors, we need to calculate the number of combinations for each pair of colors as well as the individual colors. The possible pairs with their respective numbers of combinations are blue-red, blue-white, and red-white. For blue-red and blue-white, he can paint 5 blue stripes and 3 stripes of the other color, while for red-white, he can paint 5 red stripes and 3 white stripes.

The combinations for each pair would be:

Blue-Red: 5 blue + 3 red

Blue-White: 5 blue + 3 white

Red-White: 5 red + 3 white

Additionally, Bred can choose to use only one color. Thus, for each of the colors blue, red, and white, there will only be one way to paint the wall.

Therefore, the total different ways Bred can paint the wall are the sum of the combinations for each pair plus the individual color options:

For pair Blue-Red: 1 way

For pair Blue-White: 1 way

For pair Red-White: 1 way

Only Blue: 1 way

Only Red: 1 way

Only White: 1 way

Adding these up gives us a total of 6 different ways to paint the wall.

For the circumference, you actually multiply by 20 because of the formula πd = C [OR 2πr = C]. You meant to double the radius.

The expression that gives us the number of miles that Mr. Roberts drove on Tuesday is (42÷2) +5.

We know that Mr. Roberts drove 42 miles on Monday.

On Tuesday Mr. Roberts drove half of what he drove on Monday plus 5 miles.

If we want to know how many miles Mr. Roberts drove on Tuesday then we should divide 42÷2 to find half of 42.

42 / 2  = 21

Then we know that in addition to the 21 miles he drove 5 more miles. Then we add 21 +5 = 26 miles.

So the expression that gives us the number of miles that Mr. Roberts drove on Tuesday is:

(42÷2) +5

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Question

On Monday, Mr. Roberts drove 42 miles. On Tuesday, he drove 5 miles more than half the distance he drove on Monday. Which expression shows how you could find the distance, in miles, Mr. Roberts drove on Tuesday?( 42 ? 5 ) × 2 42 ? ( 5 × 2 ) ( 42 ÷ 2 ) ? 5 ( 42 ÷ 2 ) + 5

Answer:

P(gummy bear) = [tex]\frac{4}{11}[/tex]

Explanation:

Probability of a certain outcome can be calculated as follows:

[tex]P(certain-outcome)=\frac{number-of-occurrences-of-this-outcome}{total-number-of-possible-outcomes}[/tex]

In the given problem we have:

20 gummy bears and 35 orange slices

We want to find P(gummy bear)

This means that:

number of occurrences of desired outcome = number of gummy bears = 20

Total number of possible outcomes = gummy bears + orange slices

Total number of possible outcomes = 20 + 35 = 55

Substitute with the givens in the above formula, we get:

[tex]P(gummy-bears)=\frac{20}{55}=\frac{4}{11}[/tex]

Hope this helps :)

Final answer:

The probability of selecting a gummy bear from a bag containing 20 gummy bears and 35 orange slices is approximately 36.36%.

Explanation:

The student's question is about finding the probability of selecting a gummy bear from a bag of sweets. Given that there are 20 gummy bears and 35 orange slices in the bag, to find the probability of selecting a gummy bear, we use the formula P(gummy bear) = (number of gummy bears) / (total number of sweets). Therefore, P(gummy bear) = 20 / (20 + 35) = 20 / 55. Simplifying this, we get approximately 0.3636, which can also be expressed as a percentage, 36.36%.

The point which will lie in the solution set to the following system of inequalities is:

                          (2,5)

The system of inequality is given by:

       y>-3x+3--------(1)

and  y>x+2----------(2)

Now, the point that will lie in the solution set to the following system of inequality are the point that satisfies both the inequality.

a)

 (2,-5)

when x=2 and y= -5

then by first inequality we have:

-5>-3×2+3

i.e.

-5>-6+3

i.e.

-5>-3

which is a false identity.

This means that the point will not lie in the solution set.

b)

(-2,5)

when x= -2 and y=5

then  by first inequality we have:

5>-3×(-2)+3

i.e.

5>6+3

i.e.

5>9

which is a false identity.

Hence, option: b is incorrect.

c)

(2,5)

when x=2 and y=5

then by first inequality:

    5>-3×2+3

i.e.  5>-6+3

i.e.  5>-3

which is true

and by second identity:

      5>2+2

i.e.  5>4

which is again true.

Hence, (2,5) lie in the solution set.

d)

(-2,-5)

when x= -2 and y= -5

then by first inequality we have:

-5>-3×(-2)+3

i.e.

-5>6+3

i.e.

-5>9

which is a false identity.

Hence, the point (-2,-5) do not lie in the solution set.

Answer:

False

Step-by-step explanation:

The number of degrees of freedom associated with the t-test, when the data are gathered from a paired samples experiment with 12 pairs, is;

12 - 1 = 11

The paired samples t-test is equivalent to a one sample t-test for the mean. The degrees of freedom are obtained by subtracting one from the number of pairs;

Answer:

Option C. is the correct option.

Step-by-step explanation:

A bag contains 10 red, 6 blue and 4 green jelly beans.

A jelly bean is chosen at random from the bag then probability that the ball is blue will be = [tex]\frac{\text{Total number of blue balls}}{\text{Total number of balls in the bag}}[/tex]

P(B) = [tex]\frac{6}{20}[/tex]

Now we know that probability that the ball picked from the bag is not blue

= 1 - P(B)

= 1 - [tex]\frac{6}{20}[/tex]

= [tex]\frac{20 - 6}{20}[/tex]

= [tex]\frac{14}{20}[/tex]

= [tex]\frac{7}{10}[/tex]

Therefore, option C. is the correct option.

The probability is the ratio of non-blue jelly beans to the total, resulting in 7/10. The correct answer is C) 7/10.

To determine the probability that a randomly chosen jelly bean from the bag is not blue, we first need to find the total number of jelly beans:

Total number of jelly beans = 10 + 6 + 4 = 20

Next, we need to calculate the number of jelly beans that are not blue:

Number of non-blue jelly beans = 10 + 4 = 14

The probability of choosing a jelly bean that is not blue is given by the ratio of non-blue jelly beans to the total number of jelly beans:

Probability = Number of non-blue jelly beans / Total number of jelly beans = 14 / 20 = 7 / 10.

if you add all the x points together the girl will have more text messages