Simplify (5 + 1)^2 - (12 + 3^2) = %3.
A. 29
B. -39
C. 5
D. -63

Answer:

Step-by-step explanation:

m∠UTV = 112°  ⇒  m∠WTV = 180° - 112° = 68°

sin(68°) ≈ 0.9272

sin(∠WTV) = WV/TV

WV/10 ≈ 0.9272

WV ≈ 9.272

WV ≈ 9.3

The answer is B. Shooting. Shooting is a sport on dry land, while the other three are aquatic sports, that is, they are on or in the water.

You should use a T distribution to find the critical T value based on the level of confidence. The confidence level is often given to you directly. If not, then look for the significance level alpha and compute C = 1-alpha to get the confidence level. For instance, alpha = 0.05 means C = 1-0.05 = 0.95 = 95% confidence

Use either a table or a calculator to find the critical T value. When you find the critical value, assign it to the variable t.

Next, you'll compute the differences of each pair of values. Form a new column to keep everything organized. Sum everything in this new column to get the sum of the differences, which then you'll divide that by the sample size n to get the mean of the differences. Call this dbar (combination of d and xbar)

After that, you'll need the standard deviation of the differences. I recommend using a calculator to quickly find this. A spreadsheet program is also handy as well. Let sd be the standard deviation of the differences

The confidence interval is in the form (L, U)

L = lower bound

L = dbar - t*sd/sqrt(n)

U = upper bound

U = dbar + t*sd/sqrt(n)

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = 4 and (a, b) = (- 3, - 4) , thus

y - (- 4) = 4(x - (- 3)) , that is

y + 4 = 4(x + 3) → C

Answer:

19

Step-by-step explanation:

Inscribed Angle = 1/2 Intercepted Arc

< DBG = 1/2 ( DG)

< DBG = 1/2 ( 360 - BD - BG)

           = 1/2 ( 360 - 172 - 150)

           = 1/2 (38)

           = 19

Answer:

[tex]\boxed{3520\ ft/min}[/tex]

Step-by-step explanation:

1 miles per hour = 88 feet per minute

Multiplying both sides by 40

40 miles per hour = 88*40 ft/min

40 mi./hr = 3520 ft/min

Answer:

3520 feet/min

Step-by-step explanation:

the speed of the car in feet per minute:

first convert miles to feet ( 1 mile =5280 feet) and hours to minutes(1hr=60min.)

(40*5280)/1*60=3520 feet/min

Answer:

480 liters of natural oil

Step by step Explanation:

ratio of natural to synthetic oil

= 5:3

If 440 liters have to be made then,

Add 5 + 3 = 8

So, 5/8 of 768 liters will be = 480 liters of natural oil

and, 3/8 of 768 liters will be = 288liters of synthetic oil

Therefore, 480 liters of natural oil will be needed

Answer:

log 12 = 1.0761

Step-by-step explanation:

log 12

=log(3*2*2)

= log 3 +log 2+ log 2

=0.4771+0.3010+0.3010

=1.0761

Answer:

Log 12 = 1.0791

Step-by-step explanation:

=> log (12)

Prime Factorizing 12

=> log (2×2×3)

Using log rule : [tex]log (a*b) = log a+logb[/tex]

=> Log 2 + log 2 + log 3

Given that log 2 = 0.3010 , log 3 = 0.4771

=> 0.3010 + 0.3010 + 0.4771

=> 1.0791

Answer:

Option A is the correct option.

Step-by-step explanation:

As PW is the median.

PW = [tex] \frac{1}{2} [/tex] ( YZ + TM )

Plug the values

x = [tex] = \frac{1}{2} (5.5 + 12.1)[/tex]

Calculate the sum

x = [tex] = \frac{1}{2} \times 17.6[/tex]

Calculate the product

x = [tex] = 8.8[/tex]

Hope this helps...

Best regards!

Answer:

see below

Step-by-step explanation:

Angle C is equal to the 1/2 the difference of the two arcs

C = 1/2 ( large DC - small DC)

Large DC = ( 360 - 5x - 2)   sum of a circle is 360 degrees

Small DC = 5x-2  the central angle is equal to the intercepted arc

C = 1/2 ( 360 - 5x-2 - ( 5x -2))  Angle Formed by Two Intersecting Chords

C = 1/2 ( 360 - 2 ( 5x-2))

Distributing the 1/2

C = 180 - (5x-2)

Replacing the C with 2x+7

2x+7 = 180 - (5x-2)

Add 5x-2 to each side

2x+7  +5x-2  = 180

Antonio is correct

Combine like terms

7x +5 = 180

7x = 175

Divide by 7

x =25

Then solve for A = 5x-2

A = 5*25-2

   = 125-2

   = 123

Answer:

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

Step-by-step explanation:

From the information given :

An exit poll of 200 voters finds that 94 voted for the referendum.

How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52​? Based on your​ result, comment on the dangers of using exit polling to call elections.

This implies that ;

the Sample size n = 200

the probability p = 0.52

Let X be the random variable

So; the Binomial expression can be represented as:

X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)

Mean [tex]\mu[/tex] = np

Mean [tex]\mu[/tex]  = 200 × 0.52

Mean [tex]\mu[/tex]  = 104

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]

The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]

The standard deviation [tex]\sigma[/tex] = 7.065

However;

P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .

The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5

Now;

x = 94.5

Therefore;

[tex]z = \dfrac{x- \mu}{\sigma}[/tex]

[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]

[tex]z = \dfrac{-9.5}{7.065}[/tex]

z = −1.345

P(X< 94.5) = P(Z < - 1.345)

From the z- table

P(X ≤ 94) =  0.09012

From what we observe; There is a probability  of less than 94 people who voted for the referendum is 0.09012

Comment:

The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.

Answer:

Cuadrilátero solo significa "cuatro lados" (quad significa cuatro, lateral significa lado). Un cuadrilátero tiene cuatro lados, es bidimensional (una forma plana), cerrado (las líneas se unen) y tiene lados rectos.

Un cuadrilátero es un polígono con cuatro aristas y cuatro vértices.

Step-by-step explanation:

Answer:

  £531.52

Step-by-step explanation:

We are given the profit in week 1 and information about week 2. We are asked for the difference between week 2 profit and week 1 profit.

__

In week 2, pizza is sold 4 ways. The diagram shows the numbers of pizzas sold each way. The table shows the profit made for each way the pizza was sold. We need to add up the profits from each of the sales to find the profit for week 2.

Then the total profit in week 2 is ...

  £1514.04 -175.42 +888.94 -5.68 = £2221.88

So, profit in week 2 exceeds profit in week 1 by ...

  £2221.88 -1690.36 = £531.52 . . . more profit in week 2

Answer:

The correct option is

This is a polynomial function of degree 7 with a leading coefficient of -1

Step-by-step explanation:

Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions

Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1

Which can be expanded as follows

f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;

f(x) = -x⁷ + 2·x⁴ + 1

Which is  polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7  

Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.

it is isosceles triangle as you see

so that 62 = other unknown angle

as it is a triangle interior angles sum = 180

124 + x = 180

x = 180 - 124

x = 56

Answer:

[tex]\boxed{f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}}[/tex]

Step-by-step explanation:

[tex]f(x)=2x^2-3x[/tex]

[tex]f(x)=y[/tex]

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

Switch variables.

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

Solve for y.

Multiply both sides by 8.

[tex]8x=16y^2-24y[/tex]

Add 9 on both sides.

[tex]8x+9=16y^2-24y+9[/tex]

Take the square root on both sides.

[tex]\sqrt{8x+9} =\sqrt{16y^2-24y+9}[/tex]

Add 3 on both sides.

[tex]\sqrt{8x+9}+3 =\sqrt{16y^2-24y+9}+3[/tex]

Divide both sides by 4.

[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{\sqrt{16y^2-24y+9}+3}{4}[/tex]

Simplify.

[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y-3+3}{4}[/tex]

[tex]\frac{\sqrt{8x+9}+3}{4}= \frac{4y}{4}[/tex]

[tex]\frac{\sqrt{8x+9}+3}{4}=y[/tex]

Inverse y = [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)= \frac{\sqrt{8x+9}+3}{4}[/tex]

Answer:

[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]

Step-by-step explanation:

[tex] f^{-1}(x) = 2x^2 - 3x [/tex]

Change function notation to y.

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

Switch x and y.

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

Solve for y.

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

Complete the square on the left side. We must divide both sides by 2 to have y^2 as the leading term on the left side.

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

1/2 of 3/2 is 3/4. Square 3/4 to get 9/16.

Add 9/16 to both sides to complete the square.

[tex] y^2 - \dfrac{3}{2}y + \dfrac{9}{16} = \dfrac{x}{2} + \dfrac{9}{16} [/tex]

Find common denominator on right side.

[tex] (y - \dfrac{3}{4})^2 = \dfrac{8x}{16} + \dfrac{9}{16} [/tex]

If X^2 = k, then [tex] X = \pm \sqrt{k} [/tex]

[tex] y - \dfrac{3}{4} = \pm \sqrt{\dfrac{1}{16}(8x + 9)} [/tex]

Simplify.

[tex] y = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]

Back to function notation.

[tex] f^{-1}(x) = \dfrac{3}{4} \pm \dfrac{1}{4}\sqrt{8x + 9} [/tex]

Answer:

y=-x-2

Step-by-step explanation:

y-3=-x-5

y=-x-2

Answer:

C = 35 + 0.08t

Step-by-step explanation:

The equation is:

35 + 0.08t = C

C = Cost by month

t = cost for each additional message

Answer:

The slope is 1/3 and the y intercept is 6

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b where m is the slope and b is the y intercept

3y -x =18

Add x to each side

3y = x+18

Divide each side by 3

3y/3 = x/3 +18/3

y = 1/3x +6

The slope is 1/3 and the y intercept is 6

We need to solve for y (y = mx + b):

3y - x = 18

~Add x to both sides

3y = 18 + x

~Divide 3 to everything

y = 6 + x/3 or y = 6 + 1/3/x

So... 1/3 is the slope and 6 is the y-intercept.

Best of Luck!

Answer:

B. 6sqrt(2).

Step-by-step explanation:

Since the two legs of the right triangle are congruent, this is a 45-45-90 triangle. That means that the hypotenuse will measure xsqrt(2) units, and each leg will measure x units.

In this case, x = 6.

So, the hypotenuse is B. 6sqrt(2).

Hope this helps!

Answer with explanation:

Two or more Algebraic expressions are said to be equivalent, if both the expression produces same numerical value , when variable in the expressions are replaced by any Real number.

The two expressions are

1. 7 x +4

2. 3 x +5 +4 x =1

Adding and subtracting Variables and constants

→7 x +5=1

→7 x +5-1

→7 x +4

→ When x=2,

7 x + 4 =7×2+4

=14 +4

=18

So, Both the expression has same value =18.

→So, by the definition of equivalent expression, when ,you substitute , x by any real number the two expression are equivalent.

Correct options among the given statement about the expressions are:

1.When x = 2, both expressions have a value of 18.

2.The expressions have equivalent values for any value of x.

3.The expressions have equivalent values if x = 8.

Answer: -1.8

Step-by-step explanation:

Start at -5.5 and move the point on the number line up 3.7 spaces.

Hope it helps <3

Answer:

Your correct answer is -1.8

Step-by-step explanation:

−5.5 + 3.7

= −5.5+3.7

= −1.8

Answer: The concentration of the mixture is 0.5 p % .

Step-by-step explanation:

Given: 5 gallons of p% boric acid is mixed with 5 gallons of water.

Amount of boric acid = p% of 5 gallons

[tex]=\dfrac{p}{100}\times5\text{ gallons}= 0.05p\text{ gallons}[/tex]

Total solution : 5 +5 = 10 gallons

then, the concentration of the mixture = [tex]\dfrac{\text{Amount of boric acid in solution}}{\text{Total solution}}\times100[/tex]

[tex]=\dfrac{0.05p}{10}\times100\\\\=0.5p[/tex]

Hence, the concentration of the mixture is 0.5 p % .

Answer:

0.5p% is the answer

Answer:

Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.

Step-by-step explanation:

The coin theoretically could give a very large number of tails first so each person's probability is made up of an infinite series.

P(1st person wins) = P(H) + P(TTTH) + P(TTTTTTH) + . . . etc

= 1/2 + (1/2)^4 + (1/2)^7 + (1/2)^10 + . . .

This is a geometric series with first term a = 1/2 and common ratio r = 1/8

Using formula a/(1 - r) this is (1/2)/(7/8) = 4/7

P(2nd person wins) = P(TH) + P(TTTTH) + P(TTTTTTTH)

= (1/2)^2 + (1/2)^5 + (1/2)^8 + . . .

Geometric series with sum (1/4)/(7/8) = 2/7

P(3rd person wins) = P(TTH) + P(TTTTTH) + P(TTTTTTTTH) + . . .

= (1/2)^3 + (1/2)^6 + (1/2)^9 + . . .

Geometric series with sum (1/8)/(7/8) = 1/7

Players probabilities of winning are 4/7 , 2/7, 1/7 which of course sum to 1.

Hope this helped!

Answer:

Step-by-step explanation:

(-3)² + (-3)² = (-3)*(-3) + (-3)*(-3)

                 = 9 + 9

                 = 18

Answer:

18

Step-by-step explanation:

Sara works 46 hours per week

9 hours are overtime and 37 hours are regular time

pay rate at time and a half: 10.20∗1.5=15.30

regular hours plus overtime pay

37∗10.20=377.40

9∗15.30=137.70

Income due to tips

Total hours worked∗60per hour∗20%

46∗60∗.20=552

Weekly Income=Hourly income + tips

Weekly Income=377.40+137.70+552.00

Weekly Income=1067.10

Annual income=Weekly income∗52

Annual income=55489.20

Answer: 0.0046

Step-by-step explanation:

First, let's calculate the total number of outcomes that you can see from a pair of dice.

Each dice has 6 options, so the total number of combinations is:

6*6 = 36.

Now, the combinations that are equal to 3 are:

3 and 1

1 and 3

2 combinations.

So the probability is equal to the quotient between the number of combinations that are equal to 3, and the total number of combinations:

P = 2/36 = 0.055

Now, the combinations that are equal to 10 are:

5 and 5

4 and 6

6 and 4.

3 combinations.

Then the probability is:

P = 3/36 = 0.0833

Now, the probability of both events happening is equal to the product of the probabilities for each event, so the total probability is equal to:

P = ( 0.0833)*( 0.055) = 0.0046

Answer:

2.

Step-by-step explanation:

The slope is calculated by doing rise over run.

The rise is: 6 - 0 = 6.

The run is: 0 - (-3) = 0 + 3 = 3.

6 / 3 = 2 / 1 = 2.

Hope this helps!

Answer:

-5/24 miles

Step-by-step explanation:

The submarine descends at a rate of -5/6 miles every 4 minutes.

To find the depth of the submarine relative to sea level after the first minute, we have to multiply the rate of descent by he time spent (1 minute). That is:

[tex]\frac{\frac{-5}{6} }{4} * 1[/tex]

=> D = -5 / (6 * 4) = -5/24 miles

Therefore, the submarine's depth is -5/24 miles.

Answer:

-1 1/5

Step-by-step explanation:

I took the test and this was the correct answer :D

Answer:

Option A.3

Step-by-step explanation:

If its rise over run the fraction should be right 2 up 6 makeing a fraction of

6/2 which equals 3

The line has a slope of 3