It takes Darline 20 minutes to drive to work in light traffic. To come home when there is heavy traffic, it takes her 36 minutes. Her speed in light traffic is 24 miles per hour faster than her speed in heavy traffic. Find her speed in light traffic and in heavy traffic.

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Answer:

x = 1.117

Step-by-step explanation:

Graph the two equations:

p(x) = 5x² - 3

q(x) = 2x + 1

On the graph below, the positive point of intersection is at (1.117, 3.233).

Positive x-value = 1.117.

Answer:

y= -2/3 x - 9

Step-by-step explanation:

The slope intercept form is

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

y = -2/3 x+b

We have a point to substitute into the equation

-5 = -2/3(-6) +b

-5 = 4 +b

Subtract 4 from each side

-5-4 = 4-4+b

-9 = b

y= -2/3 x - 9

Answer:

[tex]n \geq 42[/tex]

Step-by-step explanation:

Data provided

P = 0.6

The calculation of sample size is shown below:-

Here the sampling distribution of proportion will be approximately normal, then follow the rule which is here below:-

[tex]np\geq 10\ and\ np (1 - p)\geq 10[/tex]

Now we will consider condition 2

[tex]np(1 - p)\geq \ 10[/tex]

[tex]n(0.6) (1 - 0.6) \geq \ 10[/tex]

[tex]n(0.6) (0.4) \geq\ 10[/tex]

[tex]n\geq \frac{10}{0.24}[/tex]

[tex]n \geq 41.66667[/tex]

or

[tex]n \geq 42[/tex]

Therefore for computing the required sample size we simply solve the above equation.

Answer:

Exact Form:

- 1 /8

Decimal Form:

-0.125

Answer:

- 1/8

Step-by-step explanation:

- 2⁻³ =

= - 1/2³

= - 1/8

Answer:

3 GB

Step-by-step explanation:

Since the family has used 1 GB in 10 days. With the same rate in 30 days they would have 3 GB

Answer:

None of the above

Step-by-step explanation:

Answer:

None of the Above

Step-by-step explanation:

I got it right on Khan Academy :) Have a Great Day!

Answer:

1. 3:25

2. 60:7

Step-by-step explanation:

To express the ratio in the lowest terms:

1. 360 metres to 3 kilometres

First of all, we need to convert both the terms in same unit.

Let us convert kilometres to metres for simplicity.

We know that 1 km = 1000 m

So, 3 km = 3000 m

Hence, the ratio can be represented as:

[tex]360\ m: 3000\ m\\\Rightarrow \dfrac{360}{3000}\\ \\\text{Dividing by 10:}\\\Rightarrow \dfrac{36}{300}\\\\\text{Dividing by 12:}\\\Rightarrow \dfrac{3}{25}\\\Rightarrow 3:25[/tex]

So, the simplest ratio is 3:25.

2. 2 minutes to 14 seconds​

Converting minutes to seconds.

1 minute = 60 seconds

2 minutes = 120 seconds

So, the ratio can be written as:

120 seconds : 14 seconds

Dividing by 2:

60:7

So, the simplest form is 60:7.

The answers are:

1. 3:25

2. 60:7

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

An insurance company reported that, on average claims for a certain medical procedure are $942. an independent organization constructed a 95% confidence interval of ($930, $950) for the average amount claimed for the particular medical procedure. what conclusion best evaluates the truthfulness of the number reported by the insurance company?

a) with 95% certainty, the average claim for this medical procedure is $942.

b) with 95% certainty, the average claim for this medical procedure is not $942.

c) the confidence interval is consistent with an average claim of $942 for this medical procedure

Solution:

Confidence interval is used to express how confident we are that the population parameter that we are looking for is contained in a range of given values. Looking at the given confident interval, the lower limit is $930 and the upper limit is $950. We can see that the population mean, $942 lies within these values. The correct option would be

c) the confidence interval is consistent with an average claim of $942 for this medical procedure

Answer: A

Step-by-step explanation:

(f-g)(x) means f(x)-g(x). Since we are given f(x) and g(x), we can directly subtract them.

4x+1-(x²-5)           [distribute -1]

4x+1-x²+5            [combine like terms]

4x-x²+6                [rewrite in the order of exponents]

-x²+4x+6

Answer:

20160 ways

Probability = 0.0556

Step-by-step explanation:

We have 9 different letters, so the total number of words we can make is:

[tex]Total = 9! = 362880\ words[/tex]

If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:

[tex]N = 4 * 7! = 4*7*6*5*4*3*2 = 20160\ words[/tex]

The probability is calculated by the division of the number of words we want over the total number of words:

[tex]P = N / Total = 20160 / 362880 = 0.0556[/tex]

Answer:

[tex]b.\ cos 70 =\dfrac{4}x[/tex] is the correct answer.

Step-by-step explanation:

First of all, let us label the diagram as shown in the attached figure.

OR = 20'

QS = 16'

[tex]\triangle OPQ[/tex] is the right angled triangle that we get.

[tex]\angle P=90^\circ[/tex]

[tex]\angle O =70^\circ[/tex]

From the given figure symmetry, we can clearly see that:

Side OP = OR - QS

OP = 20 - 16 = 4'

Now, let us use trigonometric identity of cosine in [tex]\triangle OPQ[/tex].

[tex]cos\theta = \dfrac{Base}{Hypotenuse}[/tex]

[tex]cosO= \dfrac{OP}{OQ}\\\Rightarrow cos70^\circ= \dfrac{4}{OQ}[/tex]

Let the distance of ramp, OQ = x'

So, the above ratio becomes:

[tex]cos70^\circ= \dfrac{4}{x}[/tex]

So, the correct answer is:

[tex]b.\ cos 70 =\dfrac{4}x[/tex]

Answer:

False

Step-by-step explanation:

2 + 3x = 5

Put x as 1.1.

2 + 3(1.1) = 5

2 + 3.3 = 5

5.3 = 5

False.

Answer:

Solution,

X=1.1

[tex]2 + 3x = 5 \\ 2 + 3 \times 1.1 = 5 \\ 2 + 3.3 = 5 \\ 5.3 = 5 \: \: \\ hence \: it \: is \: false[/tex]

Answer:

39

Step-by-step explanation:

g(5) = 3(5) + 5 = 20

f(20) = 2(20) - 1 = 39

Answer:

f ( 2 x + 1 ) = 6 x − 2

Step-by-step explanation:

Set up the composite result function.

f ( g ( x ) )

Evaluate  f ( g ( x ) )

by substituting in the value of  g  into  f

. f ( 2 x + 1 ) = 3 ( 2 x + 1 ) − 5

Simplify each term.

Apply the distributive property.

f ( 2 x + 1 ) = 3 ( 2 x )+ 3 ⋅ 1 − 5

Multiply  2  by  3 .

f ( 2 x + 1 ) = 6 x + 3 ⋅ 1 − 5

Multiply  3  by  1  .

f ( 2 x + 1 ) = 6 x + 3 − 5

Subtract  5  from  3 . f ( 2 x +1 ) = 6 x− 2

Answer:

solution,

Similar Right triangles:

[tex] \frac{c}{h} = \frac{h}{d} \\ {h}^{2} = cd \\ {y}^{2} = 4 \times 9 \\ {y = 36 }^{2} \\ y = \sqrt{ {(6)}^{2} } \\ y = 6[/tex]

Hope this helps..

Good luck on your assignment..

Answer:whats the measure of x i really need help

Step-by-step explanation:

Answer:

10 stickers.

Step-by-step explanation:

Let's say that Mandy has m stickers, and Priscilla has p stickers.

m = 1/4p

6/5(m + 28) = p + 28

6/5(1/4p + 28) = p + 28

1/4p + 28 = 5/6p + 23 and 1/3

5/6p - 1/4p = 28 - 23 and 1/3

10/12p - 3/12p = 84/3 - 70/3

7/12p = 14/3

p = (14/3)(12/7)

p = 8

At the beginning, Priscilla had 8 stickers. That means that Mandy had 1/4 * 8 = 8 / 4 = 2 stickers.

So, in the packet, there were 8 + 2 = 10 stickers.

Hope this helps!

Answer:

(6,-3)

Step-by-step explanation:

Answer:

3/5

Step-by-step explanation:

Out of the 5 cards, 3 of them are greater than 3 or less than 2 (1, 4, 5) so the answer is 3/5.

Answer:

3/5

Step-by-step explanation:

Total number of cards: 5

Cards greater than 3: 4, 5

Cards less than 2: 1

Total of (greater than 3 or less than 1): 3 cards

p(greater than 3 or less than 1) = 3/5

Answer:

the answer is: 9.25

Step-by-step explanation:

the cube root of 792 is approximately 9.252.

To find the cube root of 792, we can use the relationship between cube roots and cube numbers.

If the cube root of 99 is approximately 4.626, we can use this information to find the cube root of 792.

Let's calculate the cube root of 792 using the relationship:

(cube root of 792) = (cube root of 99) * (cube root of 8)

Since 792 is equal to 99 multiplied by 8 (792 = 99 * 8), we can rewrite the equation as:

(cube root of 792) = (4.626) * (cube root of 8)

Now, we need to find the cube root of 8:

(cube root of 8) = 2

Substituting this value back into the equation, we get:

(cube root of 792) = (4.626) * (2) = 9.252

Therefore, the cube root of 792 is approximately 9.252.

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Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 3

For the alternative hypothesis,

H1: µ > 3

This is a right tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 100

Degrees of freedom, df = n - 1 = 100 - 1 = 99

t = (x - µ)/(s/√n)

Where

x = sample mean = 3.1

µ = population mean = 3

s = samples standard deviation = 0.5

n = number of samples = 100

t = (3.1 - 3)/(0.5/√100) = 2

We would determine the p value using the t test calculator. It becomes

p = 0.024

Alpha = 1 - confidence level = 1 - 0.95 = 0.05

Since alpha, 0.05 > than the p value, 0.024, then we would reject the null hypothesis. Therefore, at 95% confidence level, it can be concluded that the mean of the population is significantly greater than 3.

Answer:

Option A

Explanation:

the ratio of radii to volume is ^3 "to the third power"

so 5^3 : 9^3 would be the ratio for volumes

125:729

Answer:

Area: 28 square ft

Perimeter: 22 ft

Step-by-step explanation:

To find the area:

A=Lw

A is area, L is length, w is width

A=4*7

A=28

The area is 28 square feet

To find the perimeter:

P=2L+2w

P=2(7)+2(4)

P=14+8

P=22

The perimeter is 22 feet.

Hope this helps!

Answer:

[tex] \frac{1}{2} {r}^{2} ( \frac{1}{2}\pi - 1)[/tex]

option D is the right option.

solution,

Area of shaded region:

Area of sector-Area of ∆

[tex] = \frac{90}{360} \times \pi {r}^{2} - \frac{1}{2} \times r \times r \\ = \frac{1}{4} \pi {r}^{2} - \frac{1}{2} {r}^{2} \\ = \frac{1}{2} {r}^{2} ( \frac{1}{2} \pi - 1)[/tex]

Hope this helps...

Good luck on your assignment..

The  expression in square units that represents the area of the shaded segment of C. Geometry is [tex]\frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]

Since we know that

The area of the shaded region = Area of the sector - an area of a triangle

So,

[tex]= \frac{90}{360} \times \pi r^2 - \frac{1}{2} \times r\times r\\\\ = \frac{1}{4}\pi r^2 - \frac{1}{2}r^2 \\\\= \frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]

hence, The  expression in square units that represents the area of the shaded segment of C. Geometry is [tex]\frac{1}{2}r^2(\frac{1}{2}\pi - 1)[/tex]

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Answer:

M = 90 for a sample of n = 100

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance or M = 90 with s sample of n = 100. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer:

-32

Step-by-step explanation:

28=-7/8w

w=-32

Answer:

c) 0.0871

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X between c and d is given by the following formula.

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

On a single day:

24 hours, so [tex]a = 0, b = 24[/tex]

8:25 P.M. is 8:25 = 8.4167h

3:30 P. M. is the equivalent to 12 + 3:30 = 15:30 = 15.5h

Probability of rain between these times:

[tex]P(8.4167 \leq X \leq 15.5) = \frac{15.5 - 8.4167}{24 - 0} = 0.2951[/tex]

On both days:

Two days, each with a 0.2951 probability

0.2951*0.2951 = 0.0871

The correct answer is:

c) 0.0871

Answer:

144

Step-by-step explanation:

Susan can pick 4 pounds of coffee beans in an hour.  Tom can pick 2 pounds of coffee beans in an hour.  Together, they can pick 6 pounds of coffee an hour.

4 + 2 = 6

There are 24 hours in a day.  Multiply the time by the amount that can be picked to find the answer.

24 × 6 = 144

Together, the maximum number of pounds of coffee beans the can pick in a day is 144 pounds.

Together they can pick a maximum of 36 pounds of coffee

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

given:

Susan can pick 4 pounds of coffee or 2 pounds of nuts.

Tom can pick 2 pounds of coffee or 4 pounds of nuts.

So, In 6 hours

Susan will pick

= 4 * 6

= 24 pounds of coffee.

In 6 hours,

Tom will pick

=2 * 6

= 12 pounds of coffee.

Hence, together they can pick a maximum of 36 pounds of coffee

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Answer:

[tex]\boxed{x^2 = 16}[/tex]

Step-by-step explanation:

Using Tangent Secant theorem:

(x)² = (2)(2+6)

x² = 2(8)

x² = 16

Answer:

  34°

Step-by-step explanation:

Because AB and CB are tangents, the measure of angle B is the supplement of the measure of arc AC:

  180° -146° = 34°

Answer:

Step-by-step explanation:

If x is increased by 50%, it means that the amount by which x is increased is

50/100 × x = 0.5 × x = 0.5x

The new value of x would be

x + 0.5x = 1.5x

If the new value is further decreased by 30%, it means that the amount by which it was decreased is

30/100 × 1.5x = 0.3 × 1.5x = 0.45x

The new value of x would be

1.5x - 0.45x = 1.05x

Therefore, the result is 1.05x

Answer:

Step-by-step explanation:

a^2+b^2=c^2

assuming that 11 and 10 are the shorter sides of the triangle

11^2+10^2=c^2

121+100=c^2

221=c^2

[tex]\sqrt{221}=\sqrt{c^2}[/tex]

this will equal 14.87 approximately

The missing side of the triangle is √221 yd .

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Let recall the Pythagorean theorem formula:

a² + b² = c²

Replacing by the values we have;

11² + 10² = c²

c² = 121 + 100

c² = 221

c = √221 yd

Therefore, the correct answer is √221 yd .

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