A distance of 30 miles on a map is represented by a 2-inch line. If the map is enlarged to 3 times its size, what will be the scale of the enlarged map?

PLEASE HELP!

Answer:

$90, $135, $189

Step-by-step explanation:

Since the first part of the ratio is two- thirds of the second, then

first part = [tex]\frac{2}{3}[/tex] × 5 = [tex]\frac{10}{3}[/tex]

The ratio is then

[tex]\frac{10}{3}[/tex] : 5 : 7

Sum the 3 parts of the ratio

[tex]\frac{10}{3}[/tex] + 5 + 7 = [tex]\frac{46}{3}[/tex]

Divide the amount to be shared by the sum to find the value of one part of the ratio.

$414 × [tex]\frac{3}{46}[/tex] = $27 ← value of 1 part of the ratio, then

[tex]\frac{10}{3}[/tex] × $27 = $90

5 × $27 = $135

7 × $27 = $189

The 3 parts are $90, $135, $189

Answer:

0.75

Step-by-step explanation:

Z-score tells the no. of standard deviations a data point is from the mean.

the formula for z score is given by

z-score= (data value - mean) / standard deviation

Given:

mean=44

standard deviation= 8

data point=50

putting the values of mean(44), standard deviation(8) and given data value(50) in the above equation

z-score= (50-44)/8

           = 6/8

           =0.75 !

Answer:

an = 5 + 2n

Step-by-step explanation:

Each time it increases by the same amount (2), so this is an arithmetic sequence:

an = a₁ + d (n - 1)

Given a₁ = 7 and d = 2:

an = 7 + 2 (n - 1)

an = 7 + 2n - 2

an = 5 + 2n

Check our answer:

n=1: a₁ = 5 + 2(1) = 7

n=2: a₂ = 5 + 2(2) = 9

n=3: a₃ = 5 + 2(3) = 11

n=4: a₄ = 5 + 2(4) = 13

The pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a sequence:

7, 9, 11, 13…

The above pattern represents the arithmetic progression.

The first term a = 7

Common difference d = 2

nth term:

a(n) = 7 + (n - 1)(2)

a(n) = 2n + 5

Thus, the pattern represents the arithmetic progression and the explicit formula for the nth term is a(n) = 2n + 5

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The product could be either less than or greater than 67,124.

If you multiplied by a negative number, you would get a negative number, which is less than a positive number such as 67,124.

If you multiplied by zero, you would get zero, which is less than a positive number such as 67,124.

If you multiplied by one, you would get 67,124, which is equal to 67,124 since they are the same number.

If you multiplied by a positive number less than one, you would get a positive number greater than zero and less than 67,124.

If you multiplied by a positive number greater than one, you would get a positive number greater than 67,124.

Answer:

2b^2

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

5a^4

Step-by-step explanation:

2a^-4

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

5b^-2

Negative exponents go to the denominator when they are in the numerator

and to the numerator when they are in the denominator

a^-4  becomes 1/a^4

1/b^-2  becomes b^2

2/5 * 1/a^4 * b^2

2*b^2 * 1/5a^4

Rewriting

2b^2

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

5a^4

Answer:

(3, 2)

Step-by-step explanation:

Given a graphical representation of a system of equation then the solution is at the point of intersection of the 2 lines, that is

solution is ( 3, 2)

Answer:

Ratio.

Step-by-step explanation:

A logarithmic function is an appropriate model because, for evenly spaced y-values, the ratio of consecutive x-values is constant. This is the correct answer to your question.

Hope this helps!!!

Kyle.

Answer:

Step-by-step explanation:

Whenever a function is logarithmic function, we get for evenly spaced y,

say y = log x

     y+d = log x1

     y+2d = log x2

We get

d = [tex]log \frac{x_1}{x} =log \frac{x_2}{x_1}[/tex]

In other words we get the ratios of consecutive x values is constant equal to the difference in consecutive y's.

Answer:

325 sq. units

Step-by-step explanation:

top shape vol.: 5*5*5=25*5=125

bottom shap vol.:8*5*5=40*5=200

combined they are 325

Answer:

325 units ³

Step-by-step explanation:

Volume of cube = Length × Width × Height

Volume of cube  = 5 × 5 × 5

Volume of cube = 125 units ³

Volume of cuboid =  Length × Width × Height

Volume of cuboid = 8 × 5 × 5

Volume of cuboid = 200 units ³

Total volume = 125 + 200 = 325 units ³

Answer: C. 0.60

Step-by-step explanation:

From the given table , the number of students are junior : 60

The total number of students = 137

The probability of selecting any junior is given by  :-

[tex]\text{P(Junior)}=\dfrac{60}{137}[/tex]

The number of juniors which who attended Jazz = 36

Then , the probability of selecting a students is junior and attends jazz is given by  :-

[tex]\text{P(Junior and Jazz)}=\dfrac{36}{137}[/tex]

Now, the conditional probability  that the student attended the jazz concert given that student is a junior  will be :-

[tex]\text{P(Jazz}|\text{Junior)}=\dfrac{\dfrac{36}{137}}{\dfrac{60}{137}}\\\\\\=\dfrac{6}{10}=0.60[/tex]

Answer: it’s 0.60

(I just took it)

Answer:

-4/15 (Fraction form) -0.26... (Decimal form)

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

when you add the numerators which are, -3 and 1, you'd end up with -2.

when you add the denominators which are, 5 and 1, you'd end up with 6.

so that would give you -2/6.

when you simplify that you end up with -1/3.

x= -4/3 + 2/3 square root of 13 or x= -4/3 + -2/3 square root of 13 !!

Answer:

Step-by-step explanation:

3x² + 8x = 12

3x² + 8x - 12 = 0

a=3, b=8, and c=-12.  Solving with quadratic formula:

x = [ -b ± √(b² - 4ac) ] / 2a

x = [ -8 ± √(8² - 4(3)(-12)) ] / 2(3)

x = (-8 ± √208) / 6

x = (-8 ± 4√13) / 6

x = -4/3 ± 2/3 √13

Answer:

Identity Property of Addition.

Answer:

Reason which completes the proof of step 4 is:

Identity property of addition

Step-by-step explanation:

-(a+b)+a= -b

= -a+ (-b)+a   (distributive property)

= -a+a+(-b)     (Commutative property of Addition)

= 0+ (-b)        (Additive inverse property)

= -b         (Identity property of addition)

(Identity property of addition says that if 0 is the identity element and a is any element

Then, a+0=0+a=a)

So, reason which completes the proof of step 4 is:

Identity property of addition

To solve the equation 1 3/5(t-6)=-0.4, first distribute 1 3/5 to the terms inside the parentheses. Then, multiply both sides of the equation by the reciprocal of 8/5 to isolate the variable t. Finally, simplify the equation to find the solution t = 5.75.

To solve the equation 1 3/5(t-6)=-0.4, we can follow these steps:

Therefore, the solution to the equation is t = 5.75.

Final answer:

To solve the equation 1 3/5(t-6)=-0.4, distribute the 1 3/5 first and then simplify the equation by adding and subtracting terms to isolate t. The final solution is t = 2.

Explanation:

To solve the equation 1 3/5(t-6)=-0.4, we can begin by distributing the 1 3/5 to the terms inside the parentheses:

1 3/5(t-6) = 1 3/5 * t - 1 3/5 * 6 = 8/5t - 18/5

Now, we can rewrite the equation as:

8/5t - 18/5 = -0.4

Next, we can get rid of the fraction by multiplying both sides of the equation by 5:

5(8/5t - 18/5) = 5(-0.4)

After simplifying, we get:

8t - 18 = -2

Now, add 18 to both sides of the equation:

8t - 18 + 18 = -2 + 18

Simplifying further, we have:

8t = 16

Finally, divide both sides of the equation by 8 to solve for t:

t = 16/8

Therefore, the solution to the equation is t = 2.

Answer:

n = 19

Step-by-step explanation:

22n = 418

Divide both sides by 22.

n = 19

Answer:

(I'm guessing the question is asking how much money Brady needs to pay.)

Step-by-step explanation:

21-5

(the original amount minus the 5 gallons he already has)

= 16.

so Brady needs 16 gallons.

and every gallon is 1.4

so 16 * 1.4

= 22.40

So brady needs 22.40 dollars.

The total cost of 16 gallons of gas is $22.4.

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 that, 21 miles per gallon for gas mileage.

When he stops at the gas station, he already has 5 gallons of gas in his tank.

So, 21-5=16 miles

He buys gas for $1.40 per gallon

Now, total cost = 16×1.40

= $22.4

Therefore, the total cost of gas is $22.4.

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Factors of 35 :

1, 5, 7, 35

Answer:

1,5

Step-by-step explanation:

There is 12 1/3-cups in 4 cups

To determine how many 1/3-cup servings are in 4 cups, you divide 4 cups by 1/3 cup per serving, resulting in 12 servings of 1/3 cup each.

The question asks how many 1/3-cup servings are in 4 cups. To find the answer, we divide the total number of cups by the size of each serving. Here, we have 4 cups total, and we want to know how many 1/3 cup servings that equates to.

To calculate:
4 cups ÷ (1/3 cup/serving) = 4 ÷ (1/3) = 4 × 3 = 12 servings.

Therefore, there are 12 servings of 1/3 cup in 4 cups.

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D

Step-by-step explanation:

2/6 is litterally right there cause it has seven lines and tge 0 doesnt count

Answer:

[tex]x=3+\frac{\sqrt{4L^{2}+1}}{L}[/tex] and [tex]x=3-\frac{\sqrt{4L^{2}+1}}{L}[/tex]

Step-by-step explanation:

we have

[tex]L=\frac{1} {\sqrt{x^2-6x + 5}}[/tex]

Solve for x

That means-----> isolate the variable x

squared both sides

[tex]L^{2} =(\frac{1} {\sqrt{x^2-6x + 5}})^{2}\\ \\L^{2}=\frac{1} {{x^2-6x + 5}}\\ \\x^2-6x + 5=\frac{1}{L^{2}}\\ \\x^2-6x=\frac{1}{L^{2}}-5\\ \\x^2-6x+9=\frac{1}{L^{2}}-5 +9\\ \\x^2-6x+9=\frac{1}{L^{2}}+4\\ \\(x-3)^2=\frac{4L^{2}+1}{L^{2}}[/tex]

Take the square root both sides

[tex](x-3)=(+/-)\sqrt{\frac{4L^{2}+1}{L^{2}}}\\ \\x=3(+/-)\frac{\sqrt{4L^{2}+1}}{L} [/tex]

therefore

[tex]x=3+\frac{\sqrt{4L^{2}+1}}{L}[/tex]

[tex]x=3-\frac{\sqrt{4L^{2}+1}}{L}[/tex]

Answer:

B. [tex]F(x)=(x+2)^4[/tex]

Step-by-step explanation:

The parent function is [tex]G(x)=x^4[/tex]

The given translation is of the form;

This shifts the graph of [tex]G(x+k)[/tex]  [tex]G(x)=x^4[/tex], k units to the left.

If this function is shifted 2 units to the left, its equation will now be

[tex]F(x)=(x+2)^4[/tex]

The correct choice is B. [tex]F(x)=(x+2)^4[/tex]

Answer:

143 desks

62 desks

108.5 hours

=  

x desks

250 hours

15500 = 108.5x

142.8 = x

Round to 143

Step-by-step explanation:

Answer:

In 250 hours 143 seats can be assembled.

Step-by-step explanation:

62 desks can be assembled in 108.5 hours.

In 108.5 hours 62 desks can be assembled.

In 1 hour [tex]\dfrac{62}{108.5}[/tex] seats can be assembled.

In 250 hours [tex]\dfrac{62}{108.5}\times 250[/tex] seats can be assembled.

In 250 hours 142.86 seats can be assembled.

Hence, In 250 hours 143 seats can be assembled. (Round to nearest whole number)

B.

At the center of the inscribed circle of the park

Answer:

B

Step-by-step explanation:

that would be B.  This circle touches each side of the triangle and has a center which is equidistant from all of the sides.

Required sοlutiοn of inequality οf -1.6 < m/-2.5 is m < 4

Here given,

We can begin by multiplying bοth sides οf the inequality by -2.5:

[tex]$-1.6\lt \sm < {\frac{m}{-2.5}}$[/tex]

Sο the sοlutiοn tο the inequality is m < 4.

[tex]$\begin{array}{l}{{\rm -1.6 < \dfrac{m}{-2.5}}}\\\\ {{\rm -1.6\times\left(-2.5\right) \gt > m}}\\\\ {{\rm 4\gt > m}}\end{array}$[/tex]

Tο graph this sοlutiοn, we can plοt a number line with an οpen circle at 4, since m is nοt equal tο 4. Then we shade the part οf the number line tο the left οf 4, indicating all values οf m that satisfy the inequality.

The graph shοws that all values οf m tο the left οf 4, including 4 itself, satisfy the inequality.

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To solve the inequality -1.6 < m/-2.5, we multiply both sides by -2.5 and reverse the inequality sign, resulting in m being less than 4. This solution can be graphed on a number line with an open circle at 4 and shading to the left.

To solve the inequality -1.6 < m/-2.5, we need to manipulate the inequality to isolate the variable m.

First, multiply both sides of the inequality by -2.5 to get m by itself. Remember, when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. So:

To graph this solution, draw a number line and make an open circle at 4, indicating that 4 is not included in the solution. Then, shade everything to the left of 4 to represent all the numbers that are less than 4.

Answer:

Choice C is correct

Step-by-step explanation:

We use the law of exponents in this problem;

[tex](a^{b})^{2}=a^{b}*a^{b}[/tex]

Therefore,

[tex](9^{\frac{1}{2} })^{2}=9^{\frac{1}{2} }*9^{\frac{1}{2} }[/tex]

Since the base is the same, that is 9, we simply add the exponents 1/2;

[tex]9^{\frac{1}{2}+\frac{1}{2} }[/tex]

one-half plus one-half is equal to unity and any number raised to one is simply equal to the given number;

[tex]9^{1}=9[/tex]

Answer:

It would take 4 men 37 hrs and 12 mins to complete the same task.

step-by-step explanation:

Let X be the time the four men would use to complete the task.

From the question, 6 men completed a task in 24 hrs and 48 mins

But

[tex]24 \: hrs \: 48 \: mins = 24(60mins) + 48 \: mins=1488 \: mins[/tex]

Using ratio and proportion

[tex]6 \: men:1488 \: mins[/tex]

[tex]4 men:x\:mins[/tex]

if more, less divides and if less, more divides.

4 men required more time to complete the task

Hence:

[tex]x = \frac{6}{4} \times 1488 \: mins[/tex]

[tex]x = 2232 \: mins[/tex]

x = 37 hrs 12 mins

Answer: 1/8

Step-by-step explanation: There is 1/4 of a chance of spinning a red, and 1/2 of a chance of getting a heads. Multiply these numbers.

1/4 x 1/2 = 1/8

There is a 1/8 chance of this outcome.

Answer:

C = 16pi

Step-by-step explanation:

Since we are evaluating for the circumference, we plug in the r. Since r=8, we get 2*pi*8 or 16pi.

answer should be C gl btw

I think this is the answer X = 3 + 1/2y

The solutions for the system of equations are:

[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]

To solve the system of equations[tex]\(x^2 + y^2 = 6\)[/tex] and [tex]\(x^2 - y = 6\)[/tex], we can use substitution or elimination method. Let's solve it using the substitution method:

Given equations:

1.[tex]\(x^2 + y^2 = 6\)[/tex]

2.[tex]\(x^2 - y = 6\)[/tex]

From equation 2, we can express [tex]\(x^2\) as \(y + 6\):[/tex]

[tex]\[x^2 = y + 6\][/tex]

Now, substitute [tex]\(x^2 = y + 6\)[/tex] into equation 1:

[tex]\[y + 6 + y^2 = 6\][/tex]

Rearrange this equation:

[tex]\[y^2 + y + 6 = 6\][/tex]

Subtract 6 from both sides:

\[y^2 + y = 0\][tex]\[y^2 + y + 6 = 6\][/tex]

Factor out y:

[tex]\[y(y + 1) = 0\][/tex]

So, either [tex]\(y = 0\)[/tex] or [tex]\(y + 1 = 0\)[/tex] , which means[tex]\(y = 0\)[/tex]  or [tex]\(y = -1\).[/tex]

Now, substitute these values of y back into equation 2 to find the corresponding values of x.

For [tex]\(y = 0\):[/tex]

[tex]\[x^2 - 0 = 6\][/tex]

[tex]\[x^2 = 6\][/tex]

[tex]\[x = \pm \sqrt{6}\][/tex]

For [tex]\(y = -1\):[/tex]

[tex]\[x^2 - (-1) = 6\][/tex]

[tex]\[x^2 + 1 = 6\][/tex]

[tex]\[x^2 = 5\][/tex]

[tex]\[x^2 = 5\][/tex]

So, the solutions for the system of equations are:

[tex]\[ (x, y) = (\sqrt{6}, 0), (-\sqrt{6}, 0), (\sqrt{5}, -1), (-\sqrt{5}, -1) \][/tex]

The system has four solutions: [tex]\((\sqrt{6}, 0)\), \((- \sqrt{6}, 0)\), \((\sqrt{5}, -1)\), and \((- \sqrt{5}, -1)\).[/tex]

Complete question:

Choose the solution(s) of the following system of equations:

x2 + y2 = 6

x2 – y = 6

Answer:

x^3-10 is greater

Step-by-step explanation:

3(6)+5=18+5=23

6^3-10=206

206>23

The eggs are approximately 2.1 and which each turtle does not lay 113 they lay 123 eggs each year around which you subtract it all up and it comes out to 120.9.then the you divide all up which gives you your answer to your problem.

Final answer:

The volume of one spherical green turtle egg with a diameter of 4.1 cm is approximately 36.2 cubic centimeters. The total volume of 113 such eggs is about 4091.6 cubic centimeters when rounded to the nearest tenth.

Explanation:

To calculate the volume of one green turtle egg, we use the formula for the volume of a sphere, which is V = 4/3 πr³, where r is the radius of the sphere. Since the egg has a diameter of 4.1 centimeters, the radius is half of that, which is 2.05 centimeters. Plugging this value into the formula gives us V = 4/3 π(2.05 cm)³ ≈ 36.2 cubic centimeters when rounded to the nearest tenth.

Next, we calculate the total volume of eggs laid by one turtle. Since each turtle lays 113 eggs, the total volume is 113 × 36.2 cm³ = 4091.6 cm³, which rounds to 4091.6 cubic centimeters.