What are the roots of x in -10x^2 + 12x − 9 = 0

Answer:

Probability that one of the giftcards will go to a student athlete and one will go to a freshman = 26.4%

Step-by-step explanation:

At Central High School, 55% of students play a school sport. Also, 24% of the student population is in ninth grade. No ninth graders are allowed to play school sports. If two students are selected at random to receive a gift card, what is the probability that one will go to a student athlete and one will go to a freshman? Write the answer as a percent rounded to the nearest tenth of a percent.

Solution

Probability that a student plays a school sport, that is, probability that a student is a student athlete = P(S) = 55% = 0.55

Probability that a student is in the ninth grade, that is, probability that a student is a freshman = P(F) = 24% = 0.24

It was given that no freshman is allowed to play sports, hence, it translates that the event that a student is a student athlete and the event that a student is a freshman are mutually exclusive.

P(S n F) = 0

If two students are then picked at random to receive a gift card, we require the probability that one will go to a student athlete and one will go to a freshman.

Probability that the first one goes to a student athlete = P(S) = 0.55

Probability that the second one goes to a freshman ≈ 0.24

Probability that the first one goes to a freshman = P(F) = 0.24

Probability that the second one goes to a student athlete ≈ 0.55

Probability that one will go to a student athlete and one will go to a freshman

= (0.55 × 24) + (0.24 × 0.55)

= 0.132 + 0.132

= 0.264

= 26.4% in percent to the nearest tenth.

Hope this Helps!!

Answer:

You can do this two ways

1. Divide 170 into 4 parts and multiply by 3.

170/4=42.5

42.5 x 3 = 127.5 so 127.5 is the answer

2. 3/4=0.75

170 x 0.75 = 127.5

or 170/1 x 3/4 = 510/4 = 127 1/2

127 1/2 = 127.5 because 1 divided by 2 is 0.5__127 + 0.5 = 127.5

Hope this helps

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Let's arrange it into slope-intercept form.

2x - y = 4

y = 2x - 4

We are looking for a line with slope of 2 and y-intercept -4. This line is Line B.

Answer:

a) H0:μ=55,000 H1:μ>55,000

b) Yes, since we can can reject the null hypothesis

Step-by-step explanation:

a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For this case;

Null hypothesis is that the starting salary will be equal to $55,000/year.

H0:μ=55,000

Alternative hypothesis is that the starting salary will be greater than $55,000/year.

H1:μ>55,000

b) Decision Rule;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

For this case;

P-value = 0.0392

α = 0.05

Since P-value < 0.05, we can reject null hypothesis.

Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.

- Yes, since we can can reject the null hypothesis

Answer:

bh

6, 17

102

51

Step-by-step explanation:

Answer:

1/2 (bh)

1/2(17)(6)

51

Answer:

10 square inches

Step-by-step explanation:

cost of a plain t-shirt = $10

cost of 1 square inch of design addition = $1.50

let there be x square inches of design

then cost of x square inches of design = x*cost of 1 square inch of design

                                                                 = 1.50*x = 1.5x

Total cost for t-shirt with x square inches of design = cost of a plain t-shirt + cost of x square inches of design   = 10 + 1.5 x

It is given that Makeeya has only $25, then total cost which can be afforded by him will be $25 only

Thus,

10 + 1.5 x = 25

=> 1.5x = 25-10 = 15

=> x = 15/1.5 = 10

Thus, Makeeya can  put 10 square inches of design on her T-shirt.

a) The percentage of women meeting the height requirement is approximately 99.99%.

b) The percentage of men meeting the height requirement is approximately 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.

First, we standardize the height requirement using the formula:

Z = (X - μ) / σ

where X is the value (height), μ is the mean, and σ is the standard deviation.

For the lower limit (57 inches):

Z_lower = (57 - 63.3) / 2.7 ≈ -2.33

For the upper limit (76 inches):

Z_upper = (76 - 63.3) / 2.7 ≈ 4.70

Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.

The percentage of women meeting the height requirement is approximately 99.99%.

b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:

For the lower limit (57 inches):

Z_lower = (57 - 67.3) / 2.8 ≈ -3.68

For the upper limit (76 inches):

Z_upper = (76 - 67.3) / 2.8 ≈ 3.11

Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.

The percentage of men meeting the height requirement is approximately 99.95%.

c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.

For men:

Z_upper_men = Z(0.95) ≈ 1.645

For women:

Z_lower_women = Z(0.05) ≈ -1.645

Using these Z-scores, we can calculate the new height requirements:

For the new lower limit:

X_lower = Z_lower_women * σ + μ

For the new upper limit:

X_upper = Z_upper_men * σ + μ

Substituting the values:

X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches

X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches

Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.

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a) The percentage of women meeting the height requirement is 99.99%.

b) The percentage of men meeting the height requirement is 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) For women meeting the height requirement:

Given: Mean (μ) = 63.3 in.

Standard Deviation (σ) = 2.7 in.

So, Minimum height requirement:

= 4 ft 9 in

= 4 * 12 + 9

= 57 inches

and, Maximum height requirement:

= 6 ft 4 in

= 6 * 12 + 4

= 76 inches

We will calculate the Z-scores for these heights using the formula:

Z = (x - μ) / σ

For the minimum height requirement:

[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70

So, the the area between -2.33 and 4.70.

Thus, the percentage is  99.99%.

b) For men meeting the height requirement:

Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.

Minimum height requirement: 4 ft 9 in = 57 inches

Maximum height requirement: 6 ft 4 in = 76 inches

For the minimum height requirement:

[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11

So, the area between -3.68 and 3.11.

Thus, the percentage is 99.95%.

c) For the new height requirements:

For men:

[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645

For women:

[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645

For the new lower limit:

[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]

For the new upper limit:

[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]

Substituting the values:

[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]

           = 58.53 inches

and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]

                     = 71.78 inches

Therefore, the new height at least 58.5 inches and at most 71.8 inches.

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Answer:

(a) 5* 10¹⁰ (b) 5* 10⁴ particles / m²

Step-by-step explanation:

Solution

(a) We find the number of particles that is created

Now,

The energy will change into particles of masses that is averaging  200 MeV/c²

The number of particles that were created is stated as follows:

n = Ec/Er

Ec =This is the cosmic energy

Er =The rest mass energy

Thus, we  replace 10¹⁰ with Ec and (0.200 GeV/c²)c² for Er

This gives us the following:

n = 10¹⁰ GeV/ (0.200 GeV/c²)c²

= 5* 10¹⁰

Hence the number of particle created is 5* 10¹⁰

(b) We now find how many particles are there per square meter

Thus,

n/m² = 5* 10¹⁰ particles/(1000 m)²

= 5* 10⁴ particles / m²

Hence, the particles that are there per square meter is 5* 10⁴ particles / m²

Note: Kindly find an attached copy of the complete question to this solution below.

Answer:

80 km/h

Step-by-step explanation:

2 h 30 min = 2.5 h

Average speed = distance/time= 200 km/2.5 h = 80 km/h

Answer:

Step-by-step explanation:

What function ?

Answer: The monthly mortgage payment is $640

Step-by-step explanation:

The cost of the house is $159,000

The down payment made is 20%. This means that the amount paid as down payment is

20/100 × 159000 = 31800

The balance to be paid would be

159000 - 31800 = $127200

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the amount of the loan

r represents the annual rate.

n represents number of monthly payments. Therefore

a = $127200

r = 0.044/12 = 0.0037

n = 12 × 30 = 360

Therefore,

P = 127200/[{(1+0.0037)^360]-1}/{0.0037(1+0.0037)^360}]

P = 127200/[{(1.0037)^360]-1}/{0.0037(1.0037)^360}]

P = 127200/{3.779 -1}/[0.0037(3.779)]

P = 127200/(2.779/0.0139823)

P = 127200/198.75127840198

P = $640

Step-by-step explanation:

Simplifying

f(x) = 2cos(3x)

Multiply f * x

fx = 2cos(3x)

Remove parenthesis around (3x)

fx = 2cos * 3x

Reorder the terms for easier multiplication:

fx = 2 * 3cos * x

Multiply 2 * 3

fx = 6cos * x

Multiply cos * x

fx = 6cosx

Solving

fx = 6cosx

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Divide each side by 'x'.

f = 6cos

Simplifying

f = 6cos

Answer:

the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Step-by-step explanation:

Let assume that n should represent the number of the students

SO, [tex]\bar x[/tex] can now be the sample mean of number of students  in GPA's

To obtain n such that [tex]P( \bar x \leq 2.3 ) \leq .04[/tex]

⇒ [tex]P( \bar x \geq 2.3 ) \geq .96[/tex]

However ;

[tex]E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D[/tex]

[tex]E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D[/tex]

Similarly;

[tex]D\int\limits^4_2(2+ e^{-x}) dx = 1[/tex]

⇒ [tex]D*(2x-e^{-x} ) |^4_2 = 1[/tex]

⇒ [tex]D*4.117 = 1[/tex]

⇒ [tex]D= \dfrac{1}{4.117}[/tex]

[tex]\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103[/tex]

∴  [tex]Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711[/tex]

Now; [tex]P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)[/tex]

Using Chebysher one sided inequality ; we have:

[tex]P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}[/tex]

So; [tex](\omega = \bar x - \mu)[/tex]

⇒ [tex]E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}[/tex]

∴ [tex]P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}[/tex]

To determine n; such that ;

[tex]\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}[/tex]

⇒ [tex]n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}[/tex]

[tex]n \geq 16.83125[/tex]

Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Answer:

360 x 30% = answer

30% = 30/100 = 0.3

360 x 0.3 = 108

108 is the answer

Hope this helps

Step-by-step explanation:

Answer:

108 pages

Step-by-step explanation:

30% of 360=108

360*.30=108

Answer:

L(xyz) = ( 1 , 3 , -7 )

L = x + 3y - 7z -3

Step-by-step explanation:

f (x,y,z) = xy + 2yz - 3xz

f (3,1,0) = (3) (1) + 2 (1) (0) - 3 (3) (0)

f (3,1,0) = 3

fx = y - 3z

f (3,1,0) = (1) - 3 (0)

fx = 1

fy = x + 2z

f (3,1,0) = (3) - 2 (0)

fy = 3

fz = 2y - 3x

f (3,1,0) = 2 (1) - 3 (3)

fz = -7

Answer:

The inter-decile range of IQ is 40.96.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 100, \sigma = 16[/tex]

First decile:

100/10 = 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 100}{16}[/tex]

[tex]X - 100 = -1.28*16[/tex]

[tex]X = 79.52[/tex]

Ninth decile:

9*(100/10) = 90th percentile, which is X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 100}{16}[/tex]

[tex]X - 100 = 1.28*16[/tex]

[tex]X = 120.48[/tex]

Interdecile range:

120.48 - 79.52 = 40.96

The inter-decile range of IQ is 40.96.

Answer:

step 3 is wrong

Step-by-step explanation:

i know it because i did the unit test review

Answer:

D

ヾ(•ω•`)o

Step-by-step explanation:

Answer:

Distance from the base of the cliff to the point on the ground = 7608 feet

Step-by-step explanation:

Given: Height of the cliff is 532 feet, angle of depression from the top of the cliff to a point on the ground is equal to 4 degrees.

To find: distance from the base of the cliff to the point on the ground

Solution:

In ΔABC,

[tex]\angle ACB=4^{\circ}[/tex]  (Alternate interior angles)

For any angle [tex]\theta[/tex], [tex]\tan \theta =[/tex] side opposite to angle/side adjacent to angle

[tex]\tan C=\frac{AB}{BC}[/tex]

Put [tex]AB=532\,,\,\angle C=4^{\circ}[/tex]

[tex]\tan 4^{\circ}=\frac{532}{BC}\\\\BC=\frac{532}{\tan 4^{\circ}}\\\\=7607.95\\\\\approx 7608\,\,feet[/tex]

Distance from the base of the cliff to the point on the ground = 7608 feet

Answer:

Find the sales (in units) needed to earn a profit of $262,500

Step-by-step explanation:

hope this is helpful to you bro

Answer:

12.672

Step-by-step explanation:

Answer: 37.376

Step-by-step explanation: Because  4.672 x 8 is  37.376

Answer:

a rigt angle is a total of 90 degrees so subtratct 51 from 90 and you get 39 degrees.

Answer:

D

Step-by-step explanation:

The volume of pyramid = 1/3 wlh

Where w = width, l = length and h = height

While,

The volume of rectangular prism = wlh

So,

The volume of pyramid = 1/3(the volume of prism)

Answer:

n = -1

Step-by-step explanation:

So first subtract 9 to both sides

8n = -n - 9

Now you want the n on one side and the constant on the other

so add the single n to the n side

9n = -9

Divide 9 to both sides to solve for n

n = -1

Answer:

You would move 10 units to the right from zero on the x-axis.

The given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).

A coordinate plane is a two-dimensional surface formed by two number lines. It is formed when a horizontal line (the X-axis) and a vertical line (the Y-axis) intersect at a point called the origin. The numbers on a coordinate grid are used to locate points.

The given coordinate point (10, 8).

The distance of any point from the x-axis is called the x-coordinate.

In the point (10, 8), 10 units from the x-axis

Therefore, the given point is 10 units from zero, when you move on the x-axis to reach the point (10, 8).

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Answer:

Yes,these two functions are the inverse of each other.

Step-by-step explanation:

They way of finding if two functions ([tex]f(x)\,\,and\,\,g(x)[/tex] ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:

[tex]f(x) \,o \,g(x)=f(g(x))=x[/tex]

in our case:

[tex]f(g(x))=\frac{1}{g(x)+4} -9\\f(g(x))=\frac{1}{(\frac{1}{x+9} -4)+4}-9\\f(g(x))=\frac{1}{\frac{1}{x+9} }-9\\f(g(x))={x+9} -9\\f(g(x))=x[/tex]

The composition does render the identity, therefore, these two functions are indeed the inverse of each other

Answer:

2

Step-by-step explanation:

Set the height of the bar to 2 since there are 2 numbers between 21-40.

Answer:

2 people.

Step-by-step explanation:

34 minutes and 40 minutes were recorded.

Therefore, 2 people.

Answer:

  y = -12x

Step-by-step explanation:

We assume you're concerned with the form ...

  y = kx

Putting -12 for k gives ...

  y = -12x . . . . . the first choice

_____

Additional comment

The answer will depend somewhat on the context of the question. If you're studying proportions, then "k" is the constant of proportionality as shown above.

If you're studying function translations, then "k" is the vertical translation, as in ...

  y = m(x -h) +k

In this case, the equation y = x -12 will have a "k" value of -12.

Answer:

[tex]\sqrt{-6} \sqrt{-384}=\sqrt{(-6)(-384)}=\sqrt{2304}=48\\ a=48\\b=0[/tex]

or

[tex]a=-48\\b=0[/tex]

both solutions are correct because root square has two solutions, one positive and one negative.

Answer:

a= -48

b=0

Step-by-step explanation:

[tex]\sqrt[]{-6} = i\sqrt{6}[/tex]

[tex]\sqrt{-384} =i\sqrt{384}[/tex]

[tex](i\sqrt{6} )(i\sqrt{384} )[/tex]

[tex]i^{2} \sqrt{2304}[/tex]

(-1)(48) = -48

a + bi

a= -48

b= 0