What is the value of x in the equation 8 + 4 = 2 (x minus 1)?
A.5
B.StartFraction 11 Over 2 EndFraction
C.StartFraction 13 Over 2 EndFraction
D.7

Answer:

247

Step-by-step explanation:

Hello!

We can begin by finding the average and median before two numbers are removed.

(9 + 13 + 15 + 17 + 19 + 23 + 31 + 49) / 8  = 22

And the median!

(17 + 19)/ 2  =  18

Since we know that the average and median will increase by 2, we will have the median after removal as 20, and the average, 24.

For the average, we can see that the total must be 144, that's what 24 * 6 is.

19 must have been one of the numbers because (17 + 23) / 2  = 20.

That's 32 less than the original sum of 176.

So if one of the removed numbers is 19, the other must be 13.

13 * 19 = 247

Thus, the product of the removed numbers are [tex]\boxed{247}[/tex].

Hope this helps!

Answer: 1280

Step-by-step explanation:

The fourth term is 8 times the first term.

The fourth term = [tex]ar^3[/tex]

[tex]ar^{3} = 8a[/tex]

To find the common ratio:

∴ [tex]\frac{ar^3}{a} = \frac{8a}{a}\\[/tex]

∴ [tex]r^3 = 8\\r = 2\\[/tex]

Common ratio = 2

To find the nth number of terms = [tex]\frac{a(r^n -1)}{r-1\\}[/tex]

∴ [tex]\frac{a(2^{10} -1)}{2-1}[/tex]

∴ [tex]1023a\\[/tex]

The sum of 10 terms = 1023a

The sum of 10 terms = 2557.5

∵ 2557.5 = 1023a

∵ [tex]a = \frac{5}{2}[/tex]

To find the 10th term:

∴ [tex]ar^9\\[/tex]

∴ [tex]\frac{5}{2} *2^9[/tex]

⇒ 1280   ║ answer.

From the question given above, we were told that the fourth term is 8 times the first term. This can be written as:

T₄ = 8a

But

T₄ = ar³

a => is the first term

r => is the common ratio

Thus,

ar³ = 8a

Solving for the common ratio (r):

ar³ = 8a

Divide both side by a

r³ = 8

Take the cube root of both side

r = ³√8

r = 2

Thus, the common ratio (r) is 2

Next, we shall determine the first term (a). This can be obtained as follow:

Sum of 10th term (S₁₀) = 2557.5

Common ratio (r) = 2

Number of term (n) = 10

Sₙ = a[rⁿ – 1] / r – 1

2557.5 = a[2¹⁰ – 1] / 2 – 1

2557.5 = a[1024 – 1]

2557.5 = 1023a

Divide both side by 1023

a = 2557.5 / 1023

a = 2.5

Thus, the first term is 2.5

Finally, we shall determine the 10th term of the sequence. This can be obtained as follow:

Common ratio (r) = 2

First term (a) = 2.5

T₁₀ = ar⁹

T₁₀ = 2.5 × 2⁹

T₁₀ = 2.5 × 512

T₁₀ = 1280

Therefore, the 10th term of the sequence is 1280

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Answer:

i think it is g(x)=x^3/8 -1

Step-by-step explanation:

Final answer:

The television program finishes at 00:25 after starting at 22:45 and running for 2 hours and 40 minutes. The fraction of the program's total time taken by 8 ad breaks, each lasting 3 minutes, is 3/20 of the total program time.

Explanation:

To calculate the finish time of the television program that starts at 22:45 and is 2 hours and 40 minutes long, we add the duration of the program to the start time. Firstly, we convert 2 hours and 40 minutes into minutes only to simplify addition. That is 160 minutes (120 minutes for 2 hours and 40 minutes for the remaining time). When we add 160 minutes to 22:45, we need to be careful due to the change of day at midnight.

Adding the minutes part first, 45 minutes + 40 minutes = 85 minutes. We subtract 60 minutes to account for one full hour giving us 25 minutes and add an hour to the hour part. 22:45 therefore becomes 23:25 with an additional 1 hour to be added.

We are left with 1 hour to add to 23:25, which simply gets us to 00:25, or 25 minutes past midnight. The television program finishes at 00:25.

Calculating the Fraction of Time Taken by Ads

The program contains 8 ad breaks, each of which lasts 3 minutes. The total time taken by the ads is 8 breaks × 3 minutes per break = 24 minutes of ads.

To find the fraction of time taken by the ads, we need the total duration in minutes, which is 2 hours and 40 minutes or 160 minutes. The fraction is therefore 24/160, which simplifies to 3/20 when we divide both the numerator and the denominator by 8.

Thus, the fraction of the 2 hours and 40 minutes that is taken by ads is 3/20.

Answer:

Step-by-step explanation:

B.

nonlinear

Answer:

Step-by-step explanation:

Transformation involves changing the position of a shape

The coordinates of Y' are (-5, 5)

The vertices are given as:

X(2, 4), Y(-3, 4), and Z(-3,1)

The transformation rule is given as:

(x, y) → (x - 2, y + 1)

For vertex Y, we have:

(-3, 4) → (-3 - 2, 4 + 1)

Simplify

(-3, 4) → (-5, 5)

Hence, the coordinates of Y' are (-5, 5)

Read more about transformation at:

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Answer:

37.8metres

Step-by-step explanation:

The arc of the arrow can be modeled by the equation:

y=-0.02x²+0.65x+4

Where x is the horizontal distance (in meters) from Linda and y is the height (in meters) of the arrow.

The arrow hits the ground when its height (y) is zero.

Therefore, we determine the value(s) of x for which:

y=-0.02x²+0.65x+4=0

Using a calculator to solve the quadratic equation:

x=37.79 or -5.29

Since the distance cannot be a negative value, we ignore -5.29.

The distance from Linda when the arrow hits the ground is 37.8metres (to the nearest tenth)

Answer:

37.8 m

Step-by-step explanation:

Given:-

- The arc trajectory of the arrow is modeled by:

                    y = -0.02x^2 + 0.65x + 4

Where, x is the horizontal distance (in meters) from Linda

            y is the height (in meters) of the arrow

Find:-

How far from Linda does the arrow hit the ground? Round to the nearest tenth.

Solution:-

- We are to determine the range of the projectile trajectory of the arrow. The maximum distance "x_max" occurs when the arrow hits the ground.

- Set the trajectory height of arrow from linda , y = 0:

                   0 = -0.02x^2 + 0.65x + 4

- Solve the quadratic equation:

                   x = -5.29 m , x = 37.8 m

- The negative distance x lies at the back of Linda and hence can be ignored. The maximum distance travelled by the arrow would be = 37.8 m

Answer:

6 laps

Step-by-step explanation:

Jeffery needs to run 3 laps.

To find the number of laps that Jeffery needs to run, we can set up a proportion. We know that 1 lap is equal to 1 tenth of a mile, so we can set up the following proportion:

1 lap / 1 tenth mile = x laps / 3 fifths mile

Cross-multiplying and solving for x, we get:

x = (1 lap * 3 fifths mile) / (1 tenth mile)

x = 3 laps / 1 lap

x = 3

Therefore, Jeffery needs to run 3 laps.

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Final answer:

Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.

Explanation:

Given:

Lengths of the larger prism: 4 feet, 3 feet, 4 feet

Dimensions of the stacked prisms: 4 feet, 3 feet, 2 feet

Let: The lengths, widths, and heights of the smaller prism be L, W, and H respectively.

Two proportions:

4/L = 4/3

3/W = 3/2

Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.

Answer: 3

15(3)-15=30

45-15=30

30=30

15x-15=30

15x=45

x=3

Answer:

Step-by-step explanation:

[tex]\sf 15x-15=30[/tex]

[tex]\sf 15x-15+15=30+15[/tex]

[tex]\sf 15x=45[/tex]

[tex]\sf \frac{15x}{15}=\frac{45}{15}[/tex]

[tex]\sf x=3[/tex]

Answer:

C and D

Step-by-step explanation:

Answer:

its c and d

Step-by-step explanation:

Answer:

no it is less then

Step-by-step explanation:

2 3/4 is equal to 2.75 in decimal form and 2 4/5 is 2.80 in decimal form so 2 3/4 is less the 2 4/5

Answer:A D E

Step-by-step explanation:

Answer:

Can i have breainliest.

Answer:

The volume of the sculpture is 12 cubic units

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the volume of the L-shaped figure

The volume is given by

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the figure

we have

[tex]h=1\ units[/tex]

The area of the base B is equal to the area of the complete square (3 units by 3 units)  minus the area of the interior square (2 units by 2 units)

[tex]B=3^2-2^2=5\ units^2[/tex]

so the volume of the L-shaped figure is equal to

[tex]V=(5)(1)=5\ units^3[/tex]

step 2

Find the volume of the sculpture

we know that

The volume of the sculpture is equal to the volume of the L-shaped figure, multiplied by two plus the volume of two unit cubes

so

[tex]V=2(5)+2(1)=12\ units^3[/tex]

Answer:

8 slices

Step-by-step explanation:

To answer this question, we first need to know the area covered by the pizza.

Since it is circular in shape, we use the formula for the area of a circle.

Mathematically area of a circle = pi * r^2

Here, we were given the diameter but we know that D = 2r or r = D/2. This shows that the radius would be 14/2 = 7 inches

Now the area of the pizza is 22/7 * 7 * 7 = 22 * 7 = 154 square inch

Now we proceed to calculate the amount in calories present in the pizza;

That would be 154 * 14.04 = 2162.16 calories

one slice has 270 calories; The number of slices in 2162.16 calories would be 2162.16/270 = 8.008 which is approximately 8 slices

Answer:

Total length of the rectangle = 14+14= 28cm

width= 7 cm

Area of the rectangle = 28×7cm²

= 196 cm²

Area of 2 semicircles = Area of 1 circle

= π(7)² = 3.14×49= 153.86cm²

Area of the shaded region = 196-153.86

= 42.14 cm²

Answer: 42.14 [tex]cm^2[/tex]

Step-by-step explanation:

Assuming that the width of the rectangle is 7 cm, the semi-circle's radius is also 7 cm.

Let's calculate the area of the two semi-circles, which in total makes a whole circle.

The formula for a circle is [tex]a=2\pi r^2[/tex]

Since r = 7, plug it in the formula:

[tex]a=2\pi (7)^2[/tex]

[tex]a=49\pi =153.86 cm^2[/tex]

Now, to figure out the length of the rectangle, look at the semi-circles. Their radius is 7 cm, so their diameter is 14 cm. We have two semi-circles with the diameter (14 cm), so we can say that the width is 28 cm.

Area of a rectangle: [tex]a=lw[/tex]

[tex]a=7*28=196cm^2[/tex]

To find the area of the shaded region, we subtract the area of the semi-circles to the rectangle, which should be:

[tex]196 - 153.86=42.14 cm^2[/tex]

Step-by-step explanation:

The dinner buffet offers a choice of appetizers,main courses and  desserts.

The number of appetizers available in the buffet = 4

The number of main courses available in the buffet = 5

The number of desserts available in the buffet = 4

By combinations, the possible appetizer-main course-dessert combinations are there in the dinner buffet = (4) (5) (4) = 80

Answer:

[tex]z=\frac{0.93 -0.9}{\sqrt{\frac{0.9(1-0.9)}{400}}}=2[/tex]  

[tex]p_v =P(z>2)=0.0228[/tex]  

So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who say yes is significantly higher than 0.9 or 90%.

Step-by-step explanation:

Data given and notation

n=400 represent the random sample taken

X=372 represent the number of people who say yes

[tex]\hat p=\frac{372}{400}=0.93[/tex] estimated proportion of people who say yes

[tex]p_o=0.9[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that that more than 90% of its costumers would tell their friend to buy a product from the manufacturer.:  

Null hypothesis:[tex]p\leq 0.9[/tex]  

Alternative hypothesis:[tex]p > 0.9[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.93 -0.9}{\sqrt{\frac{0.9(1-0.9)}{400}}}=2[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed for this case is [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>2)=0.0228[/tex]  

So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who say yes is significantly higher than 0.9 or 90%.

Answer:

An estimate of the probability that Jorge will make a profit is (5; 0.496)

Step-by-step explanation:

The total cost = 170x1 = $170

The payoff is $35 per $1 bet

The number of wins needed to make a profit = 170/35 = 4.86 \approx 5

Probability of winning, P(win), p = 1/38

n = 170

P(Jorge will make a profit) = P(at least 5 wins)

mean = np = 4.47

standard deviation = \sqrt{npq} = 2.09

P(X \geq 5) = 1 - P(X < 5)

P(X < A) = 1 - P(Z < (A - mean)/standard deviation)

After the application of continuity correction,

P(X \geq 5) = 1 - P(Z < (4.5 - 4.47)/2.09)

= 1 - P(Z < 0.01)

= 1 - 0.5040

P(X \geq 5 = 0.496

An estimate of the probability that Jorge will make a profit is (5; 0.496)

Answer:

probability that Jorge makes a profit is = 0.46412  

Step-by-step explanation:

Solution:-

- The number of bets made on number "3", N = 170

- He bets on each number "3", k = $1

- The winning pay-off odds : $ ( 35 : 1 )

- The probability of getting number "3" on a spin, p = 1/38

- The total amount paid (C) for n = 170 bets on number "3" are:

                 C = N*k

                 C = (170)*($1)

                 C = $170

- The probability of getting a number "3" on a spin is independent for each trial.

Denote:

- The amount received per win = $ 35

- The number of wins = r

- So the minimum "N" number of wins must be enough to match loss.

                 Amount Win = Amount Loss

                 r*$35 = C

                 r*$36 = C

                 r = $170 / 36

                 r = 4.7222 ≈ 5 wins

- So the minimum amount of wins required by r = 10 to make a profit.

- Let a random variable "X" denote the number of times Jorge spins to get number "3" - Number of wins. The probability to get a number "3" on each spin is independent for each trial. Therefore X follows Binomial distribution.

- So,                         X ~ B ( N , p )

                               X ~ B ( 170 , 1/38 )  

                               1 - p = 37 / 38

- So we need to determine that Jorge get number "3" at-least r = 5 times. Where the probability mass function for binomial distribution is given below:  

                              [tex]P ( X = r ) = ^NC_r * (p)^r * ( 1 - p )^(^N^ -^ r^ )[/tex]

So,

[tex]P ( X \geq 5 ) = 1 - P ( X \leq 4) = 1 - [ P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 )]\\\\1 - [ (37/38)^1^7^0 + 170*(1/38)*(37/38)^1^6^9 + 170C2*(1/38)^2*(37/38)^1^6^8 + \\\\170C3*(1/38)^3*(37/38)^1^6^7 + 170C4*(1/38)^4*(37/38)^1^6^6 ]\\\\1 - [ 0.01074 + 0.04935 + 0.11271 + 0.17059 + 0.19249]\\\\= 1 - 0.53588\\\\= 0.46412[/tex]

- So the probability that Jorge makes a profit is = 0.46412                                        

Note:- The normal approximation to Binomial distribution may be a less cumbersome choice; however, care must be taken to verify the conditions for normal approximation i.e

                          N*p ≥ 10

With the given data, N = 170 , p = 1/38:

                          N*p = 170/38 = 4.4737 ≤ 10

Hence, the normal approximation is an invalid choice for the data given.

Answer:

  7 hours

Step-by-step explanation:

The hourly charge was $66 -17 = $49. That charge was $7/hour so Mike had the bike for ...

  $49/($7/hour) = 7 hours.

__

You could write an equation for the total charge, then set it equal to 66 and find the solution that way. For h hours, the charge is ...

  charge = 17 + 7h

  66 = 17 +7h

  49 = 7h . . . . . . . . maybe this looks familiar

  49/7 = h = 7 . . . . divide by the coefficient of h

Mike had the bike for 7 hours.

Answer:

each child must pay $ 87.75

Step-by-step explanation:

$87.75

Step-by-step explanation:

32 kilos part:

2.70 x 32 = 86.4

0.5 part: half of 2.70 is 1.35, so just add it to 86.4

Answer:

The answer to your question is  y = 2x + 1

Step-by-step explanation:

Data

line  y = 2x + 3

point  (-2, -1)

line parallel = ?

Process

1.- Find the slope of the original line.

The slope is the coefficient of the x, then the slope is 2

         y = 2x + 3

2.- Find the equation of the parallel line using the point slope equation

        y - y1 = m(x - x1)

-Substitution

       y + 1 = 2(x + 2)

-Simplification

       y + 1 = 2x + 2

       y = 2x + 2 - 1

-Result

       y = 2x + 1

Answer:  24

Step-by-step explanation:  The first few multiples of 8 are: 8, 16, 24, 32, 40, and 48. The first multiples of 12 are: 12, 24, 36, 48, 60, and 72.

...

Step 1: List the Multiples of Each Number.

Answer:

i think, it is option c.

Answer:

2,890 meters^2 is grass

Step-by-step explanation:

First find the area of the garden

Area of a rectangle can be found using:

a=lw

a=85*50

a=4,250 meters^2

We know that 32% of the area is flowers, so we can multiply 32% and 4250

32%*4250

Convert 32% to a decimal by dividing by 100

32%/100=0.32

0.32*4250=1360

So, 1360 meters^2 is flowers.

The rest must be grass, so we can find the difference between the total area and the flowers

4250-1360=2890

So, 2,890 meters^2 is grass

Answer:

The answer to your question is 2890 m²

Step-by-step explanation:

Data

length = 85 m

width = 50 m

32% are flowers

Process

1.- Calculate the area of the garden

Area = length x width

-Substitution

Area = 85 x 50

        = 4250 m²

2.- Calculate the area of the garden that are flowers

                   4250 ----------------- 100%

                       x    ------------------  32%

                           x = (32 x 4250) / 100

                           x = 136000/100

                           x = 1360 m² are flowers

3.- Calculate the area of the garden that is grass

Area of grass = 4250 - 1360

Area of grass = 2890 m²

Answer:

sin θ = (√21) / 5

tan θ = (√21) / 2

Step-by-step explanation:

Remember the formulas for the trigonometry ratios with SohCahToa:

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

If cos θ = 2/5, then:

adjacent = 2

hypotenuse = 5

Remember all right triangles follow the Pythagorean Theorem. So if you are missing one side, you can solve.

Let's find the opposite side.

a² + b² = c²

2² + b² = 5²

4 + b² = 25

b² = 21

b = √21

opposite = √21

Now we know all three sides. Use the trigonometry ratios to find sine and tangent.

sin θ = opposite / hypotenuse

sin θ = (√21) / 5

tan θ = opposite / adjacent

tan θ = (√21) / 2

Answer:

all work is shown and pictured

Answer:

a) [tex]\sqrt{64+x^2}[/tex]

b) 15

Step-by-step explanation:

a) We know that AB = 8 and BC = x. We can use the Pythagorean Theorem, which states that for a right triangle with sides a, b, and c: [tex]a^2 +b^2=c^2[/tex] , where a and b are the shortest sides and c is the longest.

Here, AB = a = 8 and BC = b = x. So, AC = c. Then:

[tex]AB^2+BC^2=AC^2[/tex]

[tex]8^2+x^2=AC^2[/tex]

[tex]AC=\sqrt{64+x^2}[/tex]

b) We know that AC - AB = 9. Since AB = 8, then AC = 9 + 8 = 17. We also have the expression from above, so set them equal:

[tex]AC=\sqrt{64+x^2}=17[/tex]

[tex]64+x^2=289[/tex]

[tex]x^2=225[/tex]

x = 15

Hope this helps!

Answer:

sqrt(x^2 +64) = AC

x = 15

Step-by-step explanation:

We can use the Pythagorean theorem since this is a right triangle

a^2 + b^2 =c^2  a and b are the legs and c is the hypotenuse

We know the legs are x and 8

x^2 + 8^2 = AC^2

x^2 + 64= AC^2

Solving for AC

Take the square root of each side

sqrt(x^2 + 64) = sqrt(AC^2)

sqrt(x^2 +64) = AC

We are given AC - AB = 9

We know AB = 8

AC -8 =9

Add 8 to each side

AC -8+8 = 9+8

AC = 17

AC is the hypotenuse,

x^2 + 64= AC^2

x^2 +64 = 17^2

x^2 +64 = 289

Subtract 64  from each side

x^2 +64-64 = 289-64

x^2 =225

Take the square root

sqrt(x^2) = sqrt(225)

x =15

Answer:

Step-by-step explanation:

Solution:-

- We will denote:

          Number of Lions = x

          Number of bears = y

          Number of elephants = z

          Any other animal = T

- Now we will mathematically each statement given by the trainer.

Statement 1:

"7 times as many lions than other animals (not lions)."

- There were 7 times as many lions than any other animals i.e ( bears and elephants). So we can express:

                       x = 7*( x + y + T)   .... E 1

Statement 2:

"there were a seventh as many bears as other animals"

- There were 1/7 as many bears than any other animals i.e ( lions and elephants). So we can express:

                       y = (x+z+T) / 7  ... E2

- Now combine two decrypted mathematical expressions.

                       x + y + z = T

                       7T + T/7 + z = T