p(b)=1/4 p(a and b)=3/25 p(a/b(=

When x = 13, the equation that is true is option D) 5(x - 9) = 20.

To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:

A) 3(18 - x) = 67

Substituting x = 13:

3(18 - 13) = 67

3(5) = 67

15 = 67

The equation is not true when x = 13. Therefore, option A is false.

B) 4(9x) = 23

Substituting x = 13:

4(9*13) = 23

4(117) = 23

468 = 23

Again, the equation is not true when x = 13. Therefore, option B is also false.

C) 2(x - 3) = 7

Substituting x = 13:

2(13 - 3) = 7

2(10) = 7

20 = 7

Once again, the equation is not true when x = 13. Therefore, option C is false as well.

D) 5(x - 9) = 20

Substituting x = 13:

5(13 - 9) = 20

5(4) = 20

20 = 20

Finally, the equation is true when x = 13. Therefore, option D is true.

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Note: the translated questions is

X = 13, which equation is true?

The solutions to the quadratic equation are [−5/2,1/3]. Option A

Given the inequality;

6x^2≥5−13x

First, convert to quadratic equation

\(6 {x}^{2} - 5 + 13x \geqslant 0 \)

No, let's solve the quadratic equation using the factorization method

\(6 {x}^{2} + 13x - 5 \geqslant 0\)

Multiply 6 by -5 and find two factor that their product equals the number and their sum equal 13. Those two number are + 15 and -2

Substitute as 15x and 5

-2x in the inequality, we have;

\(6 {x}^{2} +15x - 2x - 5 \geqslant 0\)

Factor the common multipliers

\(3x(2x + 5) - 1(2x + 5) \geqslant 0\)

We have two expressions, written as;

\((3x - 1) (2x + 5)\geqslant 0\)

Let's solve to get the roots of x

\(3x+ 1 \geqslant 0 \)

\(x \geqslant 1/3\)

\(2x + 5 \geqslant 0\)

\(x \geqslant \frac{ - 5}{2} \)

Thus, the solutions to the quadratic equation are [−5/2,1/3]. Option A

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True, the terms power and exponent have the same meaning.

Answer:

4. 1/25

5. 1/16

6. 2/9

7. 5/567

8. 1/40

9. 2/175

10. 1/30

11. 2/5

12. 9/8

13. 4/3

14. 1

Step-by-step explanation:

sorry I only know how to do 4-14. I hope this helps you.

$225 was earned from the craft sales

and $40 was earned from the play.

Given, During a school carnival, students from the middle school raised money by selling crafts, food, game tickets, and school play admissions.

Of each dollar earned, $0.15 came from games. Craft sales earned 3 times as much as games. Food sales were 4 times the amount earned from the play.

Let the amount earned by play be x,

Now, Games earned = 0.15×500 = $75

Also, crafts earned 3×75 = $225

Now, as play earned x, then food earned 4x.

According to question,

x + 75 + 225 + 4x = 500

5x + 300 = 500

5x = 200

x = 40

So, the amount earned by Play be, $40

and the amount earned by Food be $160.

Hence, $225 was earned from the craft sales

and $40 was earned from the play.

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Answer:

a. The probability that a married couple watches the show can be calculated by multiplying the probabilities that each spouse watches the show:

P(Married couple watches the show) = P(Husband watches the show) * P(Wife watches the show) = 0.4 * 0.5 = 0.2

Step-by-step explanation:

b. The probability that a wife watches the show, given that her husband does, can be calculated using Bayes' theorem:

P(Wife watches the show | Husband watches the show) = P(Husband watches the show | Wife watches the show) * P(Wife watches the show) / P(Husband watches the show)

P(Wife watches the show | Husband watches the show) = 0.7 * 0.5 / 0.4 = 0.875

c. The probability that at least one member of a married couple will watch the show can be calculated as the sum of the probabilities that either the husband or the wife watches the show:

P(At least one member of a married couple watches the show) = P(Husband watches the show) + P(Wife watches the show) - P(Married couple watches the show) = 0.4 + 0.5 - 0.2 = 0.7

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer:Sqrt(8^2 + 3^2)

Step-by-step explanation:

ok

Area of a rectangular prism: 2(wide x deep) + 2(wide x tall) + 2(tall x deep)

Substitution

Area = 2(12 x 5) + 2(12 x 12) + 2(5 x 12)

Simplification

Area = 2(60) + 2(144) + 2(60)

Area = 120 + 288 + 120

Result

Area = 528 in^2

The possible values for a third quiz score that would give her an average between 85 and 90, inclusive is: 97 ≤ x ≤ 112.

In Mathematics, the average of these quiz scores can be calculated by using the following formula:

Average = Sum of quiz score/Number of quiz scores

Note: Let the variable q represent the student's score on the third (3rd) quiz.

Substituting the given parameters into the formula, we have the following;

Average = (75 + 83 + q)/3

Average = (158 + q)/3

This ultimately implies that, an average between 85 and 90, inclusive is given by this compound inequality:

85 ≤ (158 + q)/3 ≤ 90

Multiplying all through by 3, we have the following:

255 ≤ (158 + q) ≤ 270

Subtracting 158 from both sides of the inequality, we have the following:

97 ≤ x ≤ 112

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Answer: x ≤ 7

Step-by-step explanation:

Answer:

x\(\leq\)7

Step-by-step explanation:

4x-6\(\geq\)6x-20

First get x on one side.

So substract 6x on each side to get:

4x-6x-6\(\geq\)-20

Then add 6 on each side to get:

4x-6x\(\geq\)-14

Simplify.

-2x\(\geq\)-14

Divide each side by -2 to get x alone.

*Remember that when dividing by a negative sign is fliped.

x\(\leq\)-14/-2

Simplify.

x\(\leq\)7

Using the t-distribution, the 95% confidence interval for the mean sugar content for single servings of Alpha-Bits is (10.15, 12.45).

In this problem, we have that:

The confidence interval is:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

First, we find the number of degrees of freedom, which is one less than the sample size, thus df = 19.

Now, we have to find the critical value for a 95% confidence interval with 19 df, thus, looking at the t-table or using a calculator, t = 2.093.

Then:

\(\overline{x} - t\frac{s}{\sqrt{n}} = 11.3 - 2.093\frac{2.45}{\sqrt{20}} = 10.15\)

\(\overline{x} + t\frac{s}{\sqrt{n}} = 11.3 + 2.093\frac{2.45}{\sqrt{20}} = 12.45\)

The interval is (10.15, 12.45).

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Answer:    It's not entirely clear what is being asked for in the given question, as it is not clear what the numbers represent or what operation is being performed. If you could provide more information or context, I would be happy to try and help you.

Step-by-step explanation:

Bank A grants a shorter payment period and is the least costly, so the Ruffins should take the loan from Bank A.

In finance literature and practice, the loan interest (cost) increases with a more extended payment period.

In other words, a shorter payment period reduces the interest cost of a loan.  The loan cost is also influenced by the amount of the principal and the interest rate.

Down payment = 25%

Interest rate = 11%

Mortgage period = 25 years

2 points at closing

N (# of periods) = 300 months (25 years x 12)

I/Y (Interest per year) = 11%

PV (Present Value) = $142,500 ($190,000 - $47,500)

FV (Future Value) = $0

Results:

Period Payments (PMT) = $1,396.66

Sum of all periodic payments = $418,998

Total Interest = $276,498

Down payment = $47,500 ($190,000 x 25%)

2 points = $2,850 ($142,500 x 2%)

Sum of periodic payments = $418,998

Total costs = $469,348 ($47,500 + $2,850 + $418,998)

Down payment = 15%

Interest rate = 10%

Mortgage period = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 10%

PV (Present Value) = $161,500

FV (Future Value) = $0

Results:

Period Payments (PMT) = $1,417.28

Sum of all periodic payments = $510,220.08

Total Interest = $348,720.08

Down payment = $28,500 ($190,000 x 15%)

Sum of periodic payments = $510,220.80

Total costs = $538,720.80 ($28,500 + $510,220.80)

Thus, we can recommend the Ruffins should go for a Bank A loan that costs less than Bank B's.

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Answer:

longest side

Step-by-step explanation:

In a triangle the angle with the greatest measure is always opposite the​ longest side.

Answer:

A rough calculation or guess is approximately correct, but not exact. roughly adverb.

Step-by-step explanation:

Here is the final matching of multiplication expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173

81.4 x 32.1 ≈ 2,618

32.9 x 4.81 ≈ 158

46.7 x 31.7 ≈ 1,479

59.3 x 3.57 ≈ 212

Match each multiplication expression on the left with the best estimate of its product on the right:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9

81.4 x 32.1

32.9 x 4.81

46.7 x 31.7

59.3 x 3.57

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

Estimates for the remaining expressions:

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

Matching the expressions with their estimated products:

(80)(30) = 2,400

(30)(6) = 180

(30)(5) = 150

(60)(4) = 240

(50)(30) = 1,500

29.3 x 5.9 ≈ 173.27

81.4 x 32.1 ≈ 2,612.94

32.9 x 4.81 ≈ 158.05

46.7 x 31.7 ≈ 1,480.39

59.3 x 3.57 ≈ 211.46

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Hence, there is a 0.68 percent probability that the fifth driver will be the one that police officer summons over while wearing a safety belt.

The word "probability" derives from the Latin word "propitiate," which means "credibility, probability," from the noun probabilism in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

Part A:

The likelihood that precisely 3 drivers are buckled up can be determined using the binomial probability formula:

P(X = 3) = (5 choose 3) × (0.68)³ × (0.32)²

Where (5 choose 3) = 10 is the number of ways to choose 3 drivers out of 5.

P(X = 3) = 10 × 0.68³ × 0.32²

P(X = 3) = 0.267

Consequently, there is a 0.267 percent chance that all 3 drivers are buckled up.

Part B:

The fifth driver will be pulled by by the police officer since 4 other drivers have already been stopped. We are looking for the likelihood that the motorist is wearing a safety belt.

Since 68% of drivers are safety belt wearers, there is a 0.68 percent chance that the following motorist will be as well.

Thus, there is a 0.68 percent chance that the next vehicle the police officer pulls over is driven by a person wearing a safety belt.

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Answer:

I think AC is 6.

Step-by-step explanation:

This looks like an equilateral triangle so that means because there is a 3 on  one side of the line it should be the same on the other side of the line so 3 x 2 = 6.

Step-by-step explanation:

\(triangle \: abd \\ using \: pythagoras \: theorem \\ {hyp}^{2} = {adj}^{2} + {opp}^{2} \\ {12}^{2} = {3}^{2} + {opp}^{2} \\ 144 = 9 + {x}^{2} \\ 144 - 9 = {x}^{2} \\ 135 = {x}^{2} \\ take \: the \: square \: of \: both \: sides \\x = 11.62\)

using the opposite side of triangle and

\(using \: pythagoras \: theorem \\ {16}^{2} = {11.62}^{2} + {x}^{2} \\ 256 = 135.02 + {x}^{2} \\ 256 - 135.02 = {x}^{2} \\ 120.198 = {x}^{2} \\ take \: the \: roots \: of \: both \: sides \\ x = 10.96\)

therefore the length of line AC

\( = 3 + 10.96 \\ = 13.96\)

hope this helps

so we know that θ is between π and 3π/2, which is another of saying that θ is in the III Quadrant, and obviously its cosine will be negative.

we also know that cos(θ/2) is negative, well, that rules out the I and IV Quadrants, so most likely θ/2 is on the II Quadrant, since is smaller than θ anyway, and on the II Quadrant as we know, the sine or "y" value is positive.

\(\stackrel{\textit{Half-Angle Identities}}{ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \qquad\qquad cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+\left(-\frac{1}{9} \right)}{2}}\implies cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-\left(\frac{1}{9} \right)}{2}}\)

\(cos\left(\cfrac{\theta}{2}\right)=-\sqrt{\cfrac{~~ \frac{8}{9} ~~}{2}}\implies cos\left(\cfrac{\theta}{2}\right)=-\sqrt{\cfrac{4}{9}}\implies cos\left(\cfrac{\theta}{2}\right)=-\cfrac{2}{3} \\\\[-0.35em] ~\dotfill\)

\(sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-\left( -\frac{1}{9} \right)}{2}}\implies sin\left(\cfrac{\theta}{2}\right)=+ \sqrt{\cfrac{~~\frac{10}{9}~~}{2}}\implies sin\left(\cfrac{\theta}{2}\right)=+\cfrac{\sqrt{5}}{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{~~~a_1~\hfill a_2~~~}{\left( -\cfrac{2}{3}~~,~~ \cfrac{\sqrt{5}}{3}\right)}~\hfill\)

Answer:

  (-2/3, (√5)/3)

Step-by-step explanation:

We can use the half-angle identities to find the values of the sine and cosine of the desired angle. The desired angle is a 2nd-quadrant angle, so the sine is positive, and the cosine is negative.

  \(\sin{\left(\dfrac{\theta}{2}\right)}=\sqrt{\dfrac{1-\cos{(\theta)}}{2}}=\sqrt{\dfrac{1-(-1/9)}{2}}=\sqrt{\dfrac{5}{9}}=\dfrac{\sqrt{5}}{3}\\\\\cos{\left(\dfrac{\theta}{2}\right)}=-\sqrt{\dfrac{1+\cos{(\theta)}}{2}}=-\sqrt{\dfrac{1+(-1/9)}{2}}=-\sqrt{\dfrac{4}{9}}=-\dfrac{2}{3}\)

The coordinates of the terminal point are ...

  \((a_1,a_2)=\left(\cos{\dfrac{\theta}{2}},\sin{\dfrac{\theta}{2}}\right)=\left(-\dfrac{2}{3},\dfrac{\sqrt{5}}{3}\right)\)

The measure of angle A'B'C' in the resulting figure is approximately 142.6 degrees.

The reflection of a point (x, y) across the y-axis is (-x, y). Applying this transformation to the coordinates of A, B, and C, we get:

A' (-2, 1)

B' (-6, 1)

C' (-6, 4)

The rotation of a point (x, y) by 180 degrees counter clockwise is (-x, -y). Applying this transformation to the coordinates of A', B', and C', we get:

A'' (2, -1)

B'' (6, -1)

C'' (6, -4)

Next, we can use the law of cosines to find the measure of angle B:

A'B'C' = 180 - arccos(-7/24)

≈ 142.6 degrees

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Answer:A truncated cone and a sphere

Step-by-step explanation:

I just did it.

The combination of geometric shapes can she use to best estimate the vase's volume is a truncated cone and a sphere.

Sophie needs to determine the amount of water that will fit into her new vase, as shown below.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

We have to determine the combination of geometric shapes can she use to best estimate the vase's volume.

Therefore the combination of geometric shapes can she use to best estimate the vase's volume is a truncated cone and a sphere.

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Answer:

x=0 or x=16

Step-by-step explanation:

If

x

2

+

16

x

are the first two terms of an squared expression

(

x

+

a

)

2

=

x

2

+

2

a

x

+

a

2

then

a

=

8

x

2

+

16

x

=

0

can be written as

x

2

+

16

x

+

8

2

=

8

2

#(x+8)^2 = 64

Taking the square root

x

+

8

=

±

8

Answer:

+ 64

Step-by-step explanation:

f(x) = x² - 16x

To complete the square

add ( half the coefficient of the x- term)² to x² - 16x

f(x) = x² + 2(- 8) +(- 8)²

     = (x - 8)² + 64

     = (x - 8)² ← a perfect square

Answer:

abb_xdcb_apn come here 10th girls for studies.

Step-by-step explanation:

75.80-18.9

67.71

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

The approximate estimate of the standard deviation of the speeding ticket fines is of 12.41.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Middle 68% of speeding ticket fines on a highway fall between 93.18 and 118.

This means that 93.18 is one standard deviation below the mean and 118 is one standard deviation above the mean. That is, the difference between 118 and 93.18 is worth two standard deviations. So

\(2s = 118 - 93.18\)

\(s = \frac{(118 - 93.18)}{2}\)

\(s = 12.41\)

The approximate estimate of the standard deviation of the speeding ticket fines is of 12.41.

The sum of the expression is (-4s 9a + 4) + (2s + 2a - 8) is -2x + 11a - 4

These are expressions that are made up of variables, terms, coefficients, factors and constants.

They are also made up of operations, such as addition, multiplication, division, floor division, subtraction, bracket and parentheses.

From the information given, we have the expressions;

(-4s + 9a + 4) + (2s + 2a - 8)

expand the bracket

-4s + 9a + 4 + 2s + 2a - 8

Now, collect the like terms

-4s + 2s + 9a + 2a + 4 - 8

add or subtract the like terms

-2x + 11a - 4

Hence, the expression is -2x + 11a - 4

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