What is the sum of the series?

Answer:

141.12 cm^2

Step-by-step explanation:

A = 1/2 (b1+b2)h where b1 = 10.2, b2 = 12.2 and h = 12.6

so

A = 1/2(10.2 + 12.2) * (12.6)

A = 1/2(22.4)(12.6)

A = 141.12 cm^2

Answer:

A≈141.12

A=a+b/2(h)

true

any given point in a circle is equal distance from the center

Answer: TRUE.

Step-by-step explanation:

It knows that the distance "d" between any two points is equal to [tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex].

In a circle the distance between a point that belongs to the circumference and the center ([tex]x_0,y_0[/tex]) is always the same. Then:

[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex] is always equal to a constant called "r".

This is:

[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}=r[/tex]

Square both sides of the equality:

[tex](\sqrt{(x-x_0)^2-(y-y_0)^2})^2=r^2[/tex]

[tex](x-x_0)^2-(y-y_0)^2=r^2[/tex]

Note that we obtain the General equation of a circle.

This prove that if the distance between a given point in the plane and a collection of points is equal, then the equation of a circle is obtained.

Therefore, the statement "A circle is the collection of points in a plane that are the same distance from a given point in the plane." is true.

x+5/30 = 50/75

x+5/10 = 2

x+5 = 20

x = 15

17k−25 is the answer.

Expressions are equal if they may be simplified to the same 0.33 expression or if one of the expressions can be written just like the other. similarly, you can additionally determine if two expressions are equal when values are substituted in for the variable and both arrive at an equal solution.

Algebraic expressions are equal in the event that they constantly lead to the same result whilst you evaluate them, irrespective of what values you substitute for the variables. For instance, if x = three, then x + x + 4 = three + three + 4 = 10 and 2x + 4 = 2(3) + four = 10 additionally.

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As we know distance equals speed multiplied by time

118*2.25=265.5

Therefore the car can travel 265.5km in 2 hours 15 minutes with the speed of 118km/h

The van can travel approximately 265.5 kilometers in 2 hours and 15 minutes.

To find out how far the van can travel in 2 hours and 15 minutes, we need to use the formula:

Distance = Speed × Time

Given:

- Speed of the van = 118 km/h

- Time = 2 hours 15 minutes

First, let's convert the time to hours:

2 hours 15 minutes = 2 + 15/60 hours

= 2.25 hours

Now, we can use the formula to calculate the distance:

Distance = 118 km/h × 2.25 hours

Distance ≈ 265.5 km

Therefore, the van can travel approximately 265.5 kilometers in 2 hours 15 minutes.

ANSWER

C. 33 units^2

EXPLANATION

The area of a kite is half times product of the diagonals.

The diagonals are

3+3=6 units

and

9+2 =11 units.

The area of the kite is

[tex] = \frac{1}{2} \times 11 \times 6[/tex]

[tex] = 11 \times 3[/tex]

[tex] = 33 {units}^{2} [/tex]

The correct choice is C

The value of F in terms of K is (9K - 2298.67)/5.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, given function:

                     K = 5/9 (F + 459.67)

                   9K = 5(F + 459.67)

                   9K = 5F + 2298.67

                   9K - 2298.67 = 5F

                   F =(9K - 2298.67)/5

Thus, the value of F in terms of K is (9K - 2298.67)/5.

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To solve for F in terms of K, you can use the equation F = (9/5)(K) - 459.67.

To solve for F in terms of K, we need to isolate F on one side of the equation.

Step 1: Start with the given equation:

K = (5/9)(F + 459.67)

Step 2: Multiply both sides of the equation by 9/5 to undo the multiplication on the right side:

(9/5)(K) = F + 459.67

Step 3: Simplify the left side:

(9/5)(K) = F + 459.67

Step 4: Subtract 459.67 from both sides to isolate F:

(9/5)(K) - 459.67 = F

Therefore, F in terms of K is given by the equation F = (9/5)(K) - 459.67.

The relationship is that (P) and (T) shows how many people come in that amount of time. Sorry I dont if that will work.

The relationship between the number of people (p) and time in hours (t) is represented by the linear equation p = 25t, where m = 25 is the slope, and b = 0 is the y-intercept.

To determine the relationship between the number of people (p) who bought tickets and the time in hours (t), we can use a linear equation of the form p = mt + b, where m is the slope and b is the y-intercept.

Looking at the table, we can observe that for every 1-hour increase in time, the number of people increases by 25. This indicates that the slope (m) is 25. To find the y-intercept (b), we can use the initial point (0, 0) from the table.

Substitute these values into the equation: 0 = m(0) + b.

Solving for b, we get b = 0.

Therefore, the equation describing the relationship is p = 25t, where p is the number of people and t is the time in hours.

Step-by-step solution:

1. Identify the slope (m): From the table, the number of people increases by 25 for each 1-hour increase in time, so m = 25.

2. Find the y-intercept (b): Use the initial point (0, 0) in the equation 0 = m(0) + b to find that b = 0.

3. Write the equation: The relationship is p = 25t, where p is the number of people and t is the time in hours.

Answer:

Second Option

[tex]y = 5[/tex]

Step-by-step explanation:

A constant function is one for which the range does not change regardless of the value of the domain.

[tex]f (x_1) = f (x_2) = f (x_3) = m[/tex]

Where m is a constant.

The constant functions are horizontal lines parallel to the axis of the x

Note that

[tex]y = x[/tex] is not a constant function because the value of y changes when x changes.

x = 1, y = 1

x = 2 y = 2

[tex]x = 5[/tex] is not a constant function because the range of the function is not constant. [tex]x = 5[/tex] is a vertical line

[tex]y = 5[/tex] is a constant function, since for any of the value of x, the value of y will always be 5

Answer:

y=5

Step-by-step explanation:

Answer

1) [tex]b=101\degree[/tex]

2) [tex]m=50\degree[/tex]

3) [tex]h=79\degree[/tex]

4) [tex]g=101\degree[/tex]

5) [tex]i=51\degree[/tex]

6) [tex]j=130\degree[/tex]

Explanation

From the diagram,

[tex]b=101\degree[/tex], corresponding angles are equal.

From the diagram, m=k, corresponding angles are equal.

But k+130=180, angles on a straight line sum up to 180 degrees.

This implies that k=180-130=50

[tex]\therefore m=50\degree[/tex]

From the diagram ; [tex]h+101=180\degree[/tex],angles on a straight line sum up to 180 degrees.

[tex]\implies h=180-101\degree[/tex]

[tex]\implies h=79\degree[/tex]

From the diagram, [tex]g=101\degree[/tex] vertically opposite angles are equal.

From the triangular portion;

i+h+m=180. sum of interior angles of a triangle.

This implies that:

i+79+50=180

i+129=180

i=180-129

[tex]i=51\degree[/tex]

Finally

[tex]j=130\degree[/tex], vertically opposite angles are equal.

Answer:

Part 1) ∠b=101°

Part 2) ∠m=50°

Part 3) ∠h=79°

Part 4) ∠g=101°

Part 5) ∠i=51°

Part 6) ∠j=130°

Step-by-step explanation:

Part 1) ∠b

we know that

∠b=101° ------> by corresponding angles

Part 2) ∠m

we know that

∠m=∠k ------> by corresponding angles

and

∠k+130°=180° -----> by supplementary angles

∠k=180°-130°=50°

therefore

∠m=50°

Part 3) ∠h

we know that

∠h+101°=180° -----> by supplementary angles

∠h=180°-101°=79°

Part 4) ∠g

we know that

∠g=101° -----> by vertical angles

Part 5) ∠i

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

so

∠h+∠m+∠i=180°

substitute the values and solve for ∠i

79°+50°+∠i=180°

∠i=180°-129°=51°

Part 6) ∠j

we know that

∠j=130° -----> by vertical angles

Answer:

The statement is false

The volume of the square pyramid is [tex]V=216\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the square pyramid is equal to

[tex]V=\frac{1}{3}b^{2}h[/tex]

we have

[tex]b=9\ in[/tex]

[tex]h=8\ in[/tex]

substitute

[tex]V=\frac{1}{3}(9)^{2}(8)[/tex]

[tex]V=216\ in^{3}[/tex]

Answer:

b

Step-by-step explanation:

yes

Answer:

B

Step-by-step explanation:

If we draw another vertical line on the other side, we can split this into a rectangle and two triangles.  The width of the rectangle is 5 m, so the base of the triangle on the left is 1 m, just like the triangle on the right.

The area is therefore the sum of the areas of each shape:

A = Arectangle + 2Atriangle

A = (5 m)(3 m) + 2(½ (1 m)(3 m))

A = 18 m²

Answer:

[tex]AC=\frac{11\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Given that triangle ABC is a right angle triangle. Where angle C is a right angle. Also we have been given that BC = 11, B = 30°. Now we need to find the value of AC.

Apply formula:

[tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]

[tex]\tan\left(B\right)=\frac{AC}{BC}[/tex]

[tex]\tan\left(30^o\right)=\frac{AC}{11}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{AC}{11}[/tex]

[tex]\frac{11}{\sqrt{3}}=AC[/tex]

[tex]AC=\frac{11}{\sqrt{3}}[/tex]

or

[tex]AC=\frac{11}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}[/tex]

or

[tex]AC=\frac{11\sqrt{3}}{3}[/tex]

Hence final answer is [tex]AC=\frac{11\sqrt{3}}{3}[/tex].

Answer:

Step-by-step explanation:

The sample space should show all the possible outcomes.

The first option includes all 4 colors and both head and tails.

The second option is missing tails as an outcome.

The third option is missing blue.

The fourth option is missing tails.

So it must be the first one.

Answer:

128

Step-by-step explanation:

To create 128 different hamburgers with multiple combinations of condiments, you would need 7 different condiments. This is due to the fact that each condiment presents 2 possibilities, on the burger or not, and 2 to the power of 7 equals 128.

In this scenario, each condiment represents an option that can be either included or excluded. This means that, for each condiment, there are 2 possibilities (it's either on the burger, or it's not). The question implies that the number of possible combinations equals 128, which is 2 to the power of 7.

So, to create 128 different hamburgers, the restaurant must offer 7 different condiments. This is because 2 (possibilities for each condiment) to the power of 7 (condiments) equals 128.

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Answer:

32

Step-by-step explanation:

put the numbers in order from less to greatest

3,13,14,16,27,37,42,64,95,97

the middle numbers are 27 and 37

27+37 is 64

64 divided by 2 is 32

First put the numbers in order from least to greatest

3, 13, 14, 16, 27, 37, 42, 64, 95, 97

Median means middle so find the middle number by deleting the least and greatest number in each "layer"

3, 13, 14, 16, 27, 37, 42, 64, 95, 97

   13, 14, 16, 27, 37, 42, 64, 95

         14, 16, 27, 37, 42, 64

               16, 27, 37, 42

                     27, 37

You have two numbers left. To find the middle take the mean of these two numbers, by adding them together then dividing the sum by two

27 + 37 = 64

64 / 2 = 32

32 is the median!!!

Hope this helped!

Answer:

0.589

Step-by-step explanation:

THis is a conditional probability question. Let's look at the formula first:

P (A | B) = P(A∩B)/P(B)

" | " means "given that".

So, it means, the "Probabilty A given that B is equal to Probability A intersection B divided by probability of B."

So we want to know P (Female | Undergraduate ). This in formula is:

P (Female | Undergraduate) = P (Female ∩ Undergraduate)/P(Undergraduate)

Now,

P (Female ∩ Undergraduate) means what is common in both female and undergraduate? There are 43% female that are undergrads. Hence,

P (Female ∩ Undergraduate) = 0.43

Also,

P (Undergraduate) is how many undergrads are there? There are 73% undergrads, so that is P (undergraduate) = 0.73

plugging into the formula we get:

P (Female | Undergraduate) = P (Female ∩ Undergraduate)/P(Undergraduate)

=0.43/0.73 = 0.589

this is the answer.

Answer:

The answer is 2

Step-by-step explanation:

we know that

step 1

Estimate each coefficient:      

1.81 ≈ 2

1.2 ≈ 1

step 2

Write the product:

[tex](2*10^{4})(1*10^{2})=(2*1)*10^{4+2}=2*10^{6}[/tex]  pairs of shoes in 10 years.

Answer:

the answer is two 2

Step-by-step explanation:

Answer:

y = 37/36

Step-by-step explanation:

let's take a peek at the denominators hmmmm 5, 9, 8   hmmmm we can get an LCD of simply their product, well, that'd be 360, so then, let's multiply both sides by the LCD of 360 to do away with the denominators and proceed.

[tex]\bf \cfrac{3}{5}y+\cfrac{2}{9}=\cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{360}}{360\left( \cfrac{3}{5}y+\cfrac{2}{9} \right)=360\left( \cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8} \right)} \\\\\\ 72(3y)+40(2)=45(5)-72(2y)+45(5) \\\\\\ 216y+80=225-144y+225\implies 216y+80=450-144y \\\\\\ 216y=370-144y\implies 360y=370\implies y=\cfrac{370}{360}\implies y=\cfrac{37}{36}[/tex]

Answer:

it is 33,699

Step-by-step explanation:

you add the MSRP, then the other charges

The sticker price of the car is $33,699.

The sticker price of the car can be calculated by adding the MSRP, premium package, navigation package, and destination charge. The MSRP is $29,999, the premium package is $2500, the navigation package is $500, and the destination charge is $700.

The sticker price is calculated as follows:

Therefore, the sticker price of the car is $33,699.

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1. 8(2a+b)

2. 5(5g+3)

3. 8(3f+2)

The reverse of the distributive property involves factoring out the Greatest Common Factor (GCF) from the terms of the expression. For example, 16a + 8b becomes 8(2a + b), where 8 is the GCF.

The reverse of the distributive property involves factoring out the Greatest Common Factor (GCF) from each term in the expression to create an equivalent expression. Here's how it's done step-by-step:

Identify the GCF for all the terms in the expression.

Factor the GCF out of each term, which is essentially dividing each term by the GCF.

Write the factored expression in the form of the GCF multiplied by the remaining terms added together.

Applying this process:

For 16a + 8b, the GCF is 8, so the equivalent expression is 8(2a + b).

For 25g + 15, the GCF is 5, so the equivalent expression is 5(5g + 3).

For 24f + 16, the GCF is 8, so the equivalent expression is 8(3f + 2).

Answer:

B. (0.61)

Step-by-step explanation:

Well, first I created venn diagram to help separate my work, then I subtracted .22 from each "probability sections" then I added them up to get .61

Work explains a lot.

Hope it helped.    :)

Answer:

I think it is C. I am not sure

The correct equation that has solutions of 3 ± √5 is (x - 3)² = 5.

The solutions of the equation are given as 3 ± √5 To find an equation that has these solutions, we would look for an equation in the form (x - a)^2 = b, where the solutions to x can be found using the square root property x = √b + a or x = -√b + a. In this case, we are looking for an equation where a is 3 and b is 5 to fit the solutions provided.

Examining the options provided:

Therefore, the equation with solutions of 3 ± √5 is (x - 3)² = 5.

(3,2) is the solution

Answer:(3,2) is the solution.

Step-by-step explanation:

Answer:

About 4 times the MAD

Step-by-step explanation:

If you go in from right to left moving you finger one dot at a time then the center of the Data Set A is 42.5 beacuse you add the two numbers together (this is because you have an even number of dots) and the center of Data Set B is 20. The MAD for set A is about 5.83 the MAD for set B is about 5.83 also. Now you have to figure out the means. The mean of data set A is 42.5, the mean for data set B is 20. The difference in the means is 22.5 and if you divide the difference of the means by the MAD you will get 3.859348199, or ≈4 times the MAD

The difference of the mean is About 4 times the MAD.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations.

Data Set A is 42.5 beacuse we add the two numbers together (this is because you have an even number of dots) and the center of Data Set B is 20.

The MAD for set A is about 5.83 the MAD for set B is about 5.83 also.

Now we have to figure out the means.

The mean of data set A is 42.5, the mean for data set B is 20.

The difference in the means is 22.5 and if we divide the difference of the means by the MAD will get

3.859348199, or ≈4 times the MAD

So, the difference in the means is about 4 times the MAD

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Answer:

[tex]\$6,087.75[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$5,400\\ r=0.024\\n=12[/tex]  

substitute in the formula above  

[tex]A=\$5,400(1+\frac{0.024}{12})^{12*5}[/tex]  

[tex]A=\$5,400(1.002)^{60}=\$6,087.75[/tex]  

Answer:

120 cm^3

Step-by-step explanation:

volume = lwh

I = 4 centimeters  

w = 5 centimeters  

h = 6 centimeters

volume = (4 cm)(5 cm)(6 cm)

volume = 120 cm^3

Answer:

The number of cutters is 7

The number of screw drivers is 22

Step-by-step explanation:

Let

x-----> the number of cutters

y----> the number of screw drivers

we know that

x+y=29 ----> equation A

15.2x+2y=150.40 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (7,22)

see the attached figure

therefore

The number of cutters is 7

The number of screw drivers is 22

Answer:

48984 m^2

Step-by-step explanation:

The height(h) of cone is given by: 50 m.

Diameter of cone is: 240 m.

Also radius(r) of cone is:240/2=120 m.

The lateral surface(S) area is given by:

The lateral area of the cone comes out to be 48984 m^2.

What is lateral area?

The formula of the lateral area of cone is given by, area = pi×r×L

The amount of territory occupied by the curved surface area of a cone is known as the lateral surface area.

The lateral surface area of a cone is also in the three-dimensional plane because it is a three-dimensional form. The shape of a cone is created by stacking and rotating several triangles around an axis. Since a cone has a flat base so it has curved surafce area as well as total surface area.  A cone's lateral area is measured in square units, such as cm2, m2, in2, and so on.

Given,

Height of cone : 50m

Diameter of cone: 240m

so,it's radius will be 120m

L = [tex]\sqrt{r^{2}+h^{2}}[/tex]

L = [tex]\sqrt{120^{2} +50^{2} }[/tex]

L = 130

since,Area = pi×r×L

=3.14×120×130

=48984m^2

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Answer:

Step-by-step explanation:

Sample space {1,2,3,4,5,6}

3 to 6: {3,4,5,6}

My punctuation may not be the same as yours, but that is what they are asking for.