there are 3/4 as many boys as girls in a class of fith-graders. if there are 35 students in the class how many are girls?​

Answer:

Step-by-step explanation:

[tex]diameter=\sqrt{(5+2)^2+(5+2)^2} \\=\sqrt{49+49} \\=\sqrt{98} \\=7\sqrt{2} \\radius=\frac{7\sqrt{2} }{2} \\\approx 4.95[/tex]

Answer:

what is the value of x if figure below 80 degree and 50 degree x?

Graph D of the given function has the smallest value for b.

As per name signifies, exponents are used in exponential functions. But take note that an exponential function does not have a constant as its base and a variable as its exponent. One of the following forms can be used for an exponential function.

f (x) = aˣ

y=f(x) >0

f(x)=abˣ , where a>0

So, f(x)=abˣ

When, b<1 f(x) decreases

When, b>1 f(x) increases and the larger the b the steeper the graph

So, graph of D is increasing and is steepest

So, graph D has the smallest value for b.

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Given: We have the expression [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-1: [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-2: [tex](875\times x^5 \times y)^{1/3}[/tex]                              [break the cube root as power [tex]1/3[/tex]]

Step-3: [tex](125.7)^{1/3}\times x^{5/3} \times y^{9/3}[/tex]                    [break [tex]875=125\times7[/tex]]

                                                                     [tex]125=5^3[/tex]

Step-4: [tex](5^3)^{1/3}\times7^{1/3}\times x^{(1+2/3)}\times y^{9/3}[/tex]       [ [tex]\frac{5}{3} =1+\frac{2}{3}[/tex] ]

Step-5: [tex]5^1\times7^{1/3}\times x^1\times x^{2/3}\times y^{3}[/tex]                [break the power of [tex]x[/tex]]

Step-6: [tex]5\times x\times y^{3} \ (7^{1/3}\times x^{2/3})[/tex]

Step-7: [tex]5xy^3 \ (7x^2)^{1/3}[/tex]

Step-8: [tex]5xy^3\sqrt[3]{7x^2}[/tex]

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Answer:

Step-by-step explanation:

The theoretical probability of getting the same side every time in a single coin toss is 1/2. Since we have five independent coin tosses, we can calculate the probability of getting the same side every time by multiplying the probability of getting the same side in each toss:

(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32

Therefore, the theoretical probability of getting the same side every time in five coin tosses is 1/32, which is equivalent to 0.03125. So, the answer is (C) 0.03125.

Answer:

Step-by-step explanation:

Number of cats = 8 - 3 = 5

Fraction that are cats [tex]=\frac{5}{8}[/tex]

Answer:

The shaded region in all of the answers are equal.

Step-by-step explanation:

Since squares have equal sides, the area of each square is 12 squared or 144.

The area of the circle in A is pi*radius squared. The diameter is 12, because that is the side length of the square. This means the radius is 6 because the radius of a circle is always half the diameter. So, the area equals 36pi.

The area of the shaded region of A is 144-36pi.

In B, the diameter of each circle is half of what it was in the circles in answer A. So, the diameter is 6 and the radius is 3. The area of each circle is 9pi, and 9 pi * 4 circles is 36pi.

The area of the shaded region of B is 144-36pi.

In C, the diameter of each circle is a third of what it was in the circles in answer A. So, the diameter is 4, and the radius is 2. The area of each circle is 4pi, and 4pi * 9 circles is 36pi.

The area of the shaded region of C is 144-36pi.

Answer:

m = -4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 Points (4,7) (5,3)

We see the y decrease by 4 and the x increase by 1, so the slope is

m = -4

Answer:

-4

Step-by-step explanation:

because the slope goes down by 4 according to the table, from 7 to 3 to -1 to -5. hope that makes sense.

Hi Martin,

To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.

The total purchase cost of all three items is:

Snow shovel: $28.61

Winter coat: $23.27

Rock salt: $7.96

Total purchase cost: $59.84

Now, we apply the applicable taxes:

State tax: 5% of $59.84 = $2.99

County tax: 0.5% of $59.84 = $0.30

City tax: 2.5% of $59.84 = $1.49

Total taxes: $2.99 + $0.30 + $1.49 = $4.78

Therefore, the total purchase price is:

Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62

Answer:

Step-by-step explanation:

Area = 8 x 4 =24

Area doubled = 48

Let x be the amount we increase width and length to get area =48.

  [tex](6+x)\times (4+x)=48[/tex]

       [tex](x+6)(x+4)=48[/tex]

       [tex]x^2+10x+24=48[/tex]

       [tex]x^2+10x-24=0[/tex]

     [tex](x+12)(x-2)=0[/tex]

[tex]\text{gives }x=-12,2[/tex]

But [tex]x=-12[/tex] is not a practical solution.

So [tex]x=2[/tex] is the required solution.

We must increase the length and width by 2.

The value of the unknown in triangle is F = 90 degrees, angle D = 37 degrees, angle E = 53 degrees, f = 18.33 units, d = 11 units, and e = 14.59 units.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

Given that, angle F = 90 degrees, angle D = 37 degrees and d = 11 units.

Using the sum of interior angles of triangle we have:

angle F + angle D + angle E = 180

90 + 37 + angle E = 180

angle E = 53 degrees.

Now, using the trigonometric identities we have:

sin (37) = d / f = 11/f

f = 11 / 0.60

f = 18.33

Using tan we have:

tan (37) = d/e = 11 / e

e = 14.59

Hence, the value of the unknown in triangle is F = 90 degrees, angle D = 37 degrees, angle E = 53 degrees, f = 18.33 units, d = 11 units, and e = 14.59 units.

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Answer:

0.38

Step-by-step explanation:

There are a total of 38 pescatarians and 35 vegetarians. This is obtained by looking at the column totals for those categories and includes both males and females

There are a total of 190 participants in the survey

P(pescatarian) = 38/190

P(vegetarian) = 35/190

P(pescatarian or vegetarian)

= P(pescatarian)  + P(vegetarian)

= 38/190  + 35/190

= 73/190

= 0.3842

= 0.38 (rounded to hundredths place)

When g be continuous on [1,6], where g(1) = 18 and g(6): = 11. Does a value 1 < c < 6 exist such that g(c) = 12

The intermediate value theorem is a fundamental theorem in calculus that states that if a continuous function f(x) is defined on a closed interval [a, b], and if there exists a number y between f(a) and f(b), then there exists at least one point c in the interval [a, b] such that f(c) = y.

According to the intermediate value theorem,

since g(x) is a continuous function on the closed interval [1, 6]

since g(1) = 18 is greater than 12, and

g(6) = 11 is less than 12,

there must be at least one value c between 1 and 6 where g(c) = 12.

Therefore, we can conclude that a value of c does exist such that g(c) = 12.

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Answer:

5/3

Step-by-step explanation:

1×3=3

3+2=5

So answer is 5/3

Answer:

It is a tangent

Step-by-step explanation:

A tangent is a straight line that brushes the circumference of a circle.

Step-by-step explanation:

Hey mate, if there are no red balls inside the bag then the probabililty will be obviously 0

To find the experimental probability for each outcome, we divide the number of times the cup lands in that position by the total number of tosses:

What is a outcome?

An outcome refers to a possible result of an experiment or event that is used to calculate the probability of that result occurring.

What is meant by experimental probability?

Experimental probability is the probability of an event based on actual, repeated trials or experiments rather than theoretical or mathematical calculations.

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The absolute maximum is 56 and absolute minimum values is 24 of a function f given by f(x) = 2x³−15x² + 36x +1 on the interval [1, 5] .

A function is defined as a relationship between a set of inputs, each having an output. In short, a function is a relationship between inputs where each input relates to exactly one output. Each function has a domain and a password domain or scope. Functions are usually denoted by f(x), where x is the input.

Given that:

f(x) = 2x³ −15x²+ 36x+ 1

f'(x) = 6x² −30x + 36

Putting f'(x) = 0

⇒ 6x² − 30x+ 36 = 0

⇒ x² −5x+6 = 0

⇒ (x−2)(x−3) = 0

⇒ x=2 or 3

We are given interval [1,5]

Hence, calculating f(x) at 2, 3, 1, 5,

f(2) = 29

f(3) = 28

f(1) = 24

f(5) = 56

Hence, absolute maximum value is 56 at x=5.

Absolute minimum value is 24 at x=1.

Complete Question:

Find the absolute maximum and absolute minimum values  of a function f given by f(x)=2x³−15x² + 36x +1 on the interval [1, 5] .

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The given statement "Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars." is True. The reason for this is that O and B stars are short-lived and burn through their fuel quickly.

The reason for this is that O and B stars burn through their fuel quickly, causing them to exhaust their nuclear fuel and end their lives in a relatively short period, typically within a few tens of millions of years.

On the other hand, stars of lower mass and cooler temperatures, like G and K type stars like our sun, have longer lifetimes and take billions of years to exhaust their nuclear fuel.

Therefore, clusters without any bright, blue stars are likely to have evolved for longer periods, allowing these short-lived stars to have already expired.

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Rounding down to the nearest whole number, we can conclude that about 12 women in her age group ran faster than Joan.

A whole number is a number that is not a fraction, decimal or negative. Whole numbers include all positive integers (1, 2, 3, ...), as well as zero (0). They are also sometimes referred to as counting numbers, as they are commonly used for counting objects or items.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is a specific type of normal distribution that has been standardized to have these specific parameters, which makes it easier to calculate probabilities and perform statistical analyses.

In the given question,

We can use the standard normal distribution to solve this problem. Since Joan's finishing time was 1.84 standard deviations faster than the mean for her age group, we know that her finishing time is in the top (100% - 1.84% = 98.16%) of the distribution.

To find the number of women who ran faster than Joan, we need to find the area under the standard normal distribution curve to the right of her z-score. Using a standard normal distribution table or calculator, we can find that the area to the right of a z-score of 1.84 is 0.0322.

Therefore, approximately 395 x 0.0322 = 12.729 women in Joan's age group ran faster than her. Rounding down to the nearest whole number, we can conclude that about 12 women in her age group ran faster than Joan.

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Answer: I got you!

Step-by-step explanation:

a) Sophie's distance is given by the formula: distance = rate × time. Therefore, her distance yesterday is s × t miles.

b) Rana's time is given by the formula: time = distance ÷ rate. Therefore, her time yesterday is m ÷ r hours.

c) Sophie's time is given by the formula: time = distance ÷ rate. Let's call the time Sophie waits for Rana "w". Then we have two equations:

Sophie's distance: s × (w + t) = 20

Rana's distance: r × (w + t) = 20 - m

We can solve for "w" by substituting the second equation into the first equation:

s × (w + t) = 20 - r × (w + t) + m

(s + r) × (w + t) = 20 + m

w + t = (20 + m) ÷ (s + r)

w = (20 + m) ÷ (s + r) - t

Therefore, Sophie waits for Rana for (20 + m) ÷ (s + r) - t hours.

d) Sophie's distance tomorrow is s × 3 miles, and Rana's distance tomorrow is r × 3 miles. Therefore, the difference in distance is (s - r) × 3 miles.

Answer:

A. 1/2 ÷ 2 = 1/4 is true.

B. 1/3 ÷ 4 = 1/12 is true.

C. 1/2 ÷ 6 = 1/12 is true.

D. 1/5 ÷ 2 = 1/10 is true.

E. 1/8 ÷ 3 = 1/24 is true.

Therefore, all the quotients are true.

(please mark my answer as brainliest)

Answer:

1/3

Step-by-step explanation:

using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3

Answer: x=16, y=9

Step-by-step explanation:  Find x first. The unmarked angle underneath the x + 19 is 9x + 1 (corresponding angles so congruent so same measure as the angle below)

So the two angles add up to 180°

x+19 + 9x + 1 = 180°

combine like terms

10x + 20 = 180

subtract 20

10x = 160

divide by 10

x = 16

Now you can find the measure of the angle marked 9x+1.

9(16) + 1

= 144 + 1

= 145

Now find y. The angle marked 9x+1 is now known to be a 145° angle. So that angle with the angle marked 3y+8 must make 180°

3y + 8 + 145 = 180

combine like terms

3y + 153 = 180

subtract 153

3y = 27

divide by 3

y = 9

-Hope this helps! Thanks, have a good day :-)

The documentation "Prints all positive odd integers that are less than or equal to max" is the most appropriate documentation for the printNums procedure, as it accurately describes the behavior of the procedure. so, the option C) is correct.

This procedure uses a loop to display all positive odd integers less than or equal to the input parameter max. It starts by initializing a count variable to 1, and then uses a repeat-until loop to display the current value of count and increment it by 2 until count is greater than max.

The documentation provided is concise, clear, and accurately describes what the procedure does, making it easy for users to understand the purpose and behavior of the procedure. So, the correct answer is C).

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_____The given question is incomplete, the complete question is given below:

In the following procedure, the parameter max is a positive integer.

PROCEDURE printNums(max)

{

count ← 1

REPEAT UNTIL(count > max)

{

DISPLAY(count)

count ← count + 2

}

}

Which of the following is the most appropriate documentation to appear with the printNums procedure?

a, Prints all positive odd integers that are equal to max.

b, Prints all negative odd integers that are less than or equal to max.

c, Prints all positive odd integers that are less than or equal to max.

d, Prints all negative odd integers that are less than or equal to max.

Work Shown:

A = P*(1+r/n)^(n*t)

6700 = 5500*(1+0.045/1)^(1*t)

6700/5500 = (1.045)^t

1.218182 = (1.045)^t

log( 1.218182 ) = log(  (1.045)^t )

log( 1.218182 ) = t*log( 1.045 )

t = log(1.218182)/log(1.045)

t = 4.483724

t = 4.5

It takes about 4.5 years to reach $6700

The area is multiplied by 1/16 and the correct option is (a) The area is multiplied by 1/16.

When the radius of a circle is multiplied by 1/4, the effect on the area can be calculated using the formula A = πr², where A is the area and r is the radius. The new radius becomes (1/4)r, so the new area can be calculated by substituting (1/4)r for r in the original formula. Simplifying this expression, we get A' = π((1/4)r)² = (1/16)πr². This shows that the area is multiplied by 1/16, so the correct answer is (a) The area is multiplied by 1/16.

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Complete question:

The radius of a circle is multiplied by 1/4. Which of the following describes the effect of this change on the area?

a. The area is multiplied by 1/16.

b. The area is multiplied by 1/4.

c. The area is multiplied by 1/8.

d. The area is multiplied by 4.

The equation of the tangent line to the graph of the function at x = 7 is:    y = -1/49 x + 50/343, the equation of the normal line to the graph of the function at x = 7 is: y = 49x - (2402/7) and  slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.

a) To find the tangent line to the graph of the function at x = 7, we need to find the slope of the function at that point. We can use the derivative of the function to find the slope:

f(x) = 1/x

f'(x) = -1/x^2

So, at x = 7, the slope of the tangent line is:

m = f'(7) = -1/7^2 = -1/49

To find the equation of the tangent line, we also need a point on the line. We know that the point (7, 1/7) is on the graph of the function, so we can use that as our point. Using the point-slope form of a line, we have:

y - 1/7 = -1/49(x - 7)

Simplifying this equation, we get:

y = -1/49 x + 50/343

So the equation of the tangent line to the graph of the function at x = 7 is:

y = -1/49 x + 50/343

b) To find the normal line to the graph of the function at x = 7, we need to find a line that is perpendicular to the tangent line we found in part (a). The slope of the normal line is the negative reciprocal of the slope of the tangent line:

m(normal) = -1/m(tangent) = -1/(-1/49) = 49

Using the point-slope form of a line again, we can find the equation of the normal line that passes through the point (7, 1/7):

y - 1/7 = 49(x - 7)

Simplifying this equation, we get:

y = 49x - [(2402)/7]

So the equation of the normal line to the graph of the function at x = 7 is:

y = 49x - (2402/7)

Problem 42:

We can use the limit definition of the derivative to find the slope of the tangent line to the graph of y = 5x^3 at the point (2,40).

Using the formula for the derivative:

dy/dx = lim(h→0) [(f(x+h) - f(x))/h]

we can calculate the slope of the tangent line at x = 2.

Plugging in the given function, we get:

[tex]\frac{dy}{dx} = \lim_{h \to 0} [(5(2+h)^3 - 40) / h][/tex]

[tex]= \lim_{h \to 0} [(40 + 60h + 30h^2 + 5h^3 - 40) / h]\\= \lim_{h \to 0} [60 + 30h + 5h^2]\\= 60[/tex]

Therefore, the slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.

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