Grace runs a website that has gotten quite popular. However, its popularity seems to have
peaked, and the site is now getting 7% fewer hits each week. If Grace's site got 38,800 hits
this week, how many weekly hits can she expect it to get 7 weeks from.

The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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Answer:

y=2/3x

Or

X=3/2y

Step-by-step explanation:

3y=2x

/3. /3

y=2/3x

3y=2x

/2. /2

3/2y=x

Hopes this helps please mark brainliest

Answer:

x=3/2y

y=2/3x

Step-by-step explanation:

for x - first screen shot

for y - second screen shot

Hope that helps!

The estimate of the population proportion of defectives is 0.05.

Given that,

There are 10 different samples of 50 observations, that is, total of 500 observations.

To find : The estimate of the population proportion of defectives

And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25

Thus, the point estimate for the population proportion defectives will be,

=25/500=0.05

or just obtain the individual proportion of each sample and then take their average to obtain the same result.

Thus, the point estimate for the population proportion defectives will be 0.05

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The probability that fewer than 60 adults will work from home will be 2%.    

we have to use the Normal probability distribution to find the probability

In a normal distribution with mean μ, SD σ, z-score Z of a measure X  is given by

Z = (X-μ)/ σ

here,

15% adults work from home , So  p= 0.15

                                                       n = 500

∴  μ = np = 500(0.15) = 75

σ  = [tex]\sqrt{np(1-p)}[/tex]

σ = 7.98

Now we have  selected adults(60) less than n (500)

So using the continuity correction , the probability is P(X< 60 - 0.5)

                                                                            = P( X< 59.5)

which is the p-value of Z when X = 59.5

∴ Z = (X-μ)/ σ

Z  =  (59.5 - 75)/7.98

Z =   - 1.98

so the p-value is 0.02

0.02 = 2% probability that fewer than 60 adults will work from home.

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Answer:

f(- 5) = 7

Step-by-step explanation:

f(- 5) means what is the value of y when x = - 5

locate x = - 5 on the x- axis, go vertically up to meet the graph at (- 5, 7 ), then

f(- 5) = 7

The cost for using 24 HCF water is 47.98(in dollars) by using a linear function.

The term linear function in mathematics refers to two distinct but related concepts.

A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. The term affine function is frequently used to distinguish such a linear function from the other concept.

A linear function is a linear map in linear algebra, mathematical analysis, and functional analysis.

The monthly cost of water use is a linear function: y=mx +b, where x represents HCF and y represents the cost of using. For example, if the cost of using x=17 HCF of water is $y=36.43, this means

that is a point (17,36.43)

the cost for using x=28 HCF is $y=54.58, means

that is a point (28, 54.58)

By using the above points we find slope m,

m=((54.58-36.43)/28-17)

m=1.65

=>y=1.65x+b

Now, we have to find the b point by using above point,

36.43=1.65*17+b

36.43=28.05+b

34.63-28.05=b

b=8.38

y=1.65x+8.38

When x=24,

y=1.65(24)+8.38

y=47.98

The cost for using 24 HCF of water is 47.98

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Answer: z=-2

Step-by-step explanation:

3z+6z-30=-48

9z-30=-48

9z-30=-48+30

9z=-18

z=-2

The distance and bearing of the boat from the port areas follows;

The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.

A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.

The speed at which the Coast Guard cutter travels = 30 knots

Bearing of the Coast Guard cutter Angelica = 95°

The time the coast guard travels in the initial direction = 2 hours

The direction the Coast Guard cutter changes to = 185°

Time of traveling in the new direction = 2 hours

30 knots = 55.56 km/hr

The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km

The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km

From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle

The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15

The distance f the boat from the port is approximately 157.15 kilometers

The base angles of an isosceles right triangle are 45°

Therefore, the bearing is 95° + 45° = 150°

The bearing from the port to the boat is 150°

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The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

In this question we have been given an expression.

We need to identify the property that is used to multiply two binomials.

(3x+5)(2x+7)=2x(3x+5)+7(3x+5)

Consider two binomials,

(3x+5)(2x+7)

= (2x+7)(3x+5)                     ...............(commutative property)

= 2x(3x+5)+7(3x+5)            ................(distributive property)

Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

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Answer:

x = 20

Step-by-step explanation:

We know that a straight line is 180 degrees. We also know that the line A and B is a supplementary angle.

We subtract 180 - 110 which will come out to 70 which is the value of angle B

We know that angles D and E are 90 degrees and since D and C is 180 degrees, that means C and E is equal to 90 degrees as well.

Since B is equal to 70 degrees, we subtract 90 - 70 to get 20 degrees which is the value of x

The value of the least integer is -1/2 or -0.5.

Based on the information given, let the integers be represented as:

x

x + 1

x + 2

x + 3

Since they all add to 4, this will be:

x + x + 1 + x + 2 + x + 3 = 4

4x + 6 = 4

Collect like terms

4x = 4 - 6

4x = -2

Divide

x = -2 / 4

x = - 1/2

Therefore, the least is - 1/2

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Answer:

8:00

Step-by-step explanation:

Calculate time

It is 5:15 now.

Subtract 15 minutes

5:00

Subtract 9 hours

subtract 5 hours

12:00

Then subtract 4 hours

8:00

The rate of change of the surface area of the balloon is 32cm²/sec

We know that volume of the sphere is,

V = 4/3πr³

Given,

dV / dt = +200

r = 5cm

d(SA) / dt = ?

dV / dt = 4πr² dr/dt

80 = 4π (25) dr/dt

dr / dt = 0.8 / π

SA = 4πr²

d(SA) / dt = 8πr dr / dt

d(SA) / dt = 8π × 5 × 0.8 / π

d(SA) / dt = 32cm²/sec

Hence the rate of change of the surface area is 32cm²/sec

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Answer:

[tex]\sqrt{2}[/tex] × [tex]\sqrt{8}[/tex]   And [tex]\sqrt{2}[/tex] ×[tex]\sqrt{3}[/tex]  

Step-by-step explanation:

3x9 are both whole numbers and 0x[tex]\sqrt{5}[/tex] has only one irrational number

Answer:

---------------------------

The required number of ounces of nuts would be 1/2 in each granola bar.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

She will use 12.5 ounces of walnuts to make 25 granola bars which is given in the question.

To determine the number of ounces of nuts in each granola bar

Let the number of ounces of nuts in each granola bar would be x

As per the given situation, we can write a ratio as

12.5 ounces : 25 bars = x ounces : 1 bars

⇒ 12.5 / 25 = x / 1

⇒ 1/2 = x

⇒ x = 1/2

Thus, the required number of ounces of nuts would be 1/2 in each granola bar.

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The angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

We know that the angle-side-angle ASA Congruence theorem states that if two angles and the side between these angles of one triangle are equal to two angles and the side between then of another triangle then those two triangles are congruent.

In given triangles ABC and PQR,

∠ABC ≅ ∠PQR

BC ≅ QR

∠BCA ≅ ∠QRA

so, by ASA Congruence theorem ΔABC ≅ ΔPQR

Therefore, the angle-side-angle (ASA) Congruence theorem proves that

ΔABC and ΔPQR are congruent triangles.

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After the use of fractional exponents give us the value 8√(x²y⁴) is 2³(x²y⁴)¹/₂.

Exponent:

Exponent is refers the way of writing the words, "raised to the power". And it is used to show that a number has been raised to a certain power.

Given,

Here we have the expression 8√(x²y⁴).

Now, we need to simplify the fractional exponents.

When we rewritten the expression like the following,

=> 8√(x²y⁴)

While we looking at these expression we know that, the number 8 can be written as the multiple of 2,

So, it can be written as,

=> 8√(x²y⁴) = 2³√(x²y⁴).

So, in the simplified form it can be written as,

=>8√(x²y⁴) =  2³(x²y⁴)¹/₂.

Therefore, the simplified form is 2³(x²y⁴)¹/₂.

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Answer:

C

Step-by-step explanation:

and for graph, rate change is 10(10 units change in Y for every 1 unit change in X) whereas another function's rate change is 4

C= is y-intercept

and in graph its -6 whereas in function its -8, so graph has higher y-intercept

Graph: Rate of change = 10, y-intercept = -6

Function: Rate of change = 10, y-intercept = -8

3Justin's estimated Vo2 max is 25.8(mL*kg*min)

What is Vo2 max ?

 The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.

Here using vo2 max fomula 1.5 miles ,

=> VO2 max = 3.5+483/Time

Here Time= 11 min 25 sec = 25/60 = 0.41 min

Then time=11.42 mins. Now,

=> VO2 max = 3.5+ 483/11.41

=> VO2 max = 3.5+42.3

=>VO2 max = 25.8(mL*kg*min)

Hence His estimated Vo2 max is 25.8(mL*kg*min)

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Friday hope that this helps

Answer:

Answer:

This is in Standard form.  Did you mean scientific form?

1.47 x [tex]10^{-4}[/tex]

Step-by-step explanation:

You move the decimal so that the number is between 1 and 10.  Then since in standard form the number is much less than 1.47, you determine how muhc less my how many places you need to move the decimal to put it back in standard form.  Since you would need to move the decimal 4 places to the left, the exponent would be -4

Answer:

4f^2/3 divided 1/4f 16f^3/3 f/3 3/16f^3 3/f

✓ Lets use algebra and simplify:[tex]\frac{\frac{4f^{2}}{3}}{\frac{1}{4f}} \\=\frac{4f^{2}}{3}* \frac{4f}{1} \\=…

The amount that Kylie make as a salary after 3 years working for the company is $76000.

Her salary after t years will be 67000 + 3000t.

In this situation, Kylie was told that for each year she stays with the company, she will be given a salary raise of $3000 every years.

Her salary after three years will be:

= $67000 + ($3000 × 3)

= $67000 + $9000

= $76000

Her salary after t years will be:

= 67000 + (3000 × t)

= 67000 + 3000t

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Answer:

None of the above

Step-by-step explanation:

Answer: 14

Step-by-step explanation: 10 + (6-2) = 14

The mean sleep time is 16.54 hours per day for newborn babies

acc to our question-

The mean sleep time is 16.54 hours per day for newborn babies.

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The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

Given,

In the question:

A leading coefficient of 1, and zeros of 4 and 3 + i.

To find the polynomial function of least degree having only real coefficients.

Now, According to the question;

The function has 4 and 3 + i .

As, i's roots

So, 3 - i is also its root a leading coefficient of 1 .

So, The function of polynomial is :

f(x) = (x - 4) [tex][(x - 3)^2 + 1][/tex]

To solve the function;

f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

Hence, The polynomial function of least degree having only real coefficient is f(x) = [tex]x^3 -10x^2 +34x-40[/tex]

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The statement which is true about this equation is that: C. The equation has no solution.

In Mathematics, no solution is sometimes referred to as zero solution. Additionally, an equation is considered as having no solution when the right hand side and left hand side of the equation are not the same or equal.

This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.

From the information provided above, we have this equation:

3(-y + 7) = 3(y + 5) + 6

Opening the bracket, we have the following:

-3y + 21 = 3y + 15 + 6

Next, we would rearrange the equation by collecting like terms as follows:

-3y + 21 = 3y + 21 (no solution)

-3y - 3y = 21 - 21

-6y = 0

y = -0/6

y = 0

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Answer:

The tablet costs more than the smartphone

Step-by-step explanation:

1 year tablet = $1.50

1 year smartphone = $0.02x12months = $0.24