Jessica earns $10.35/hour at her part-time job. Usually she works 24 hours a week. If she can only put aside 30% of her earnings, about how many weeks will she need to work in
order to save money for a new cell phone at $399?
Select one:
A. 3
B. 6
C. 5
D. 4

Answer:

  a) the largest angle is 90°, making it a right triangle

  b) the shortest side is 9.5 cm long

Step-by-step explanation:

You want the largest angle and the shortest side in a triangle whose angles are in the ratio 1 : 2 : 3.

Let x represent the smallest angle. Then the other two angles are 2x and 3x. Their sum is ...

  x +2x +3x = 180°

  x = 30° . . . . . divide by 6

  3x = 90° . . . . find the largest angle

The largest angle is 90°, a right angle. So, the triangle is a right-angled triangle.

A triangle with angles of 30°, 60°, and 90° is a "special" right triangle. Its sides are in the ratio 1 : √3 : 2. That is, the shortest side is 1/2 the length of the longest side.

  shortest side = 1/2(19 cm) = 9.5 cm

The length of the shortest side in the triangle is 9.5 cm.

__

Additional comment

In case you're not familiar with the side length ratios of the 30-60-90 special triangle, you can figure the side length from the Law of Sines. That tells you ...

  a/sin(A) = b/sin(B) = c/sin(C)

where A, B, C are the angles; and a, b, c are their opposite sides.

The shortest side is opposite the smallest angle, so we have ...

  a/sin(30°) = (19 cm)/sin(90°)

  a = sin(30°)×(19 cm) = 1/2(19 cm) = 9.5 cm

The length of the shortest side is 9.5 cm.

Using proportions, it is found that there are 1.125 cups of strawberries in each pie.

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For this problem, from the ratios, we have that:

The least common multiple of 3 and 4 is 12, hence, multiplying 4 by 3, the ratio is:

Raspberries : Strawberries : Blueberries = 12 : 9 : 4

Meaning that our of 12 + 9 + 4 = 25 cups, we have that:

There amounts are for 8 pies, hence, for a single pie:

9/8 = 1.125 cups.

There are 1.125 cups of strawberries in each pie.

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Exact Distance = [tex]2\sqrt{5}[/tex] units

Approximate Distance = 4.4721 units

=================================================

Let's use the distance formula

[tex](x_1,y_1) = (3,0) \text{ and } (x_2, y_2) = (-1,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-1))^2 + (0-(-2))^2}\\\\d = \sqrt{(3+1)^2 + (0+2)^2}\\\\d = \sqrt{(4)^2 + (2)^2}\\\\d = \sqrt{16 + 4}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.4721\\\\[/tex]

The exact distance is [tex]2\sqrt{5}[/tex] units.

That approximates to about 4.4721 units.

The mean of the given data is 7.57 and the median of the given data is 8

Given that a data set i.e. Xi= 1,3,5,8,12,15,9. asked to find the mean and median of the given data.

Mean:

The mean is the average of the supplied numbers and is computed by dividing the total number of numbers by the sum of the given numbers.

Mean= [tex]\frac{sum of observation}{number of observation}[/tex]

Mean=[tex]\frac{1+3+5+8+12+15+9}{7}[/tex]

Mean=[tex]\frac{53}{7}[/tex]

Mean=7.57

The mean of the given data is 7.57

Median:

The median is a statistical metric that identifies the midway value of an ascending-ordered dataset (i.e., from smallest to largest value). The metric separates the dataset's lower and upper halves.

Arranging in ascending-order⇒1,3,5,8,9,12,15.

Then median=8

Therefore,The mean of the given data is 7.57 and the median of the given data is 8

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A translation of the equation for the surface area of this rectangular prism is given by: SA = 2(WH + LW + LH).

An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.

Mathematically, the surface area of a rectangular prism can be calculated by using this equation or formula:

SA = 2(WH + LW + LH)

Where:

In this context, we can reasonably and logically deduce that a translation of the equation for the surface area of this rectangular prism is given by:

SA = 2(WH + LW + LH).

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The solution of expression 19×50 is found as 950.

This property states that multiplying the product of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding the products together.

In other words, the distributive property requires a phrase of the form:

A (B + C) can be simplified as A (B + C) = AB + AC.

This same applies foe the subtraction;

Thus, for the given numerical;

= 19×50

Using distributive property.

= (20 - 1)×50

Open the braces;

= 20×50 - 1×50

= 1000 - 50

= 950

Therefore, the solution of the numerical 19×50 is 950.

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Answer: 40%

Step-by-step explanation:

c=class. m=men. w=women.

c=m+w

40=24+w

40-24=24-24+w

w=16

16/40=

4/10=

4*100%/10=

400%/10=40%

If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.

Using this formula to calculate the over-all reliability of the call center

Over-all reliability of the call center=Checking customer account status × Confirming orders× Stock quotes

Where:

Checking customer account status =.85

Confirming orders= .72

Stock quotes= .96

Let plug in the formula

Over-all reliability of the call center=.85×.72×.96

Over-all reliability of the call center=0.58752

Therefore If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.

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The dimensions of the rectangular traffic sign whose perimeter is 134 inches according to the task content are; 38in by 29in.

It then follows that from the task content that the dimensions of the rectangular traffic sign are to be determined.

Since the perimeter of a rectangle is given by;

P = 2(l+b)

where the length, l = b +9.

So therefore; 134 = 2(b+9 +b)

134 = 4b + 18

4b = 134 - 18

4b = 116

b = 29

In conclusion, the length, l of the traffic sign is; 29 +9

l = 38.

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Answer:

C. an = 14 + 9n

Step-by-step explanation:

The cost of having one pizza delivered is $14. Each additional pizza costs $9 more.

Let n= additional pizza

an = 14 + (9 × n)

an = 14 + 9n

The logarithmic expansion of logs(20x + 5y) by using the properties of logarithmic is log(5)+log(4x+y).

The basic logarithmic function is of the form f(x) = logₐx(r)n = logₐx, where a > 0. It is the inverse of the exponential function aⁿ = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic functions is very useful in various mathematical computations.

Given that, log(20x+5y) and we have to expand it by using the properties of logarithms. So, let's proceed to solve the question.

log(20x+5y)

we can write 20 in terms of powers like 20 = (2²)x5

log((2².5)x+5y)

log(5(2².5x/5+5y/5))

log(5(2²x+y))

log(5(4x+y))

∵ log(ab) = log(a)+log(b)

⇒log(5(4x+y)) = log(5)+log(4x+y)

Hence, on expanding log(20x+5y) by using the properties of logarithms we get log(5)+log(4x+y) as our required answer.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let the numbers be : x, x + 1 and x + 2 ~

now, according to given condition :

[tex]\qquad \sf  \dashrightarrow \: x + 2(x + 1) = 98 - 3(x + 2)[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 2x + 2 = 98 - 3x - 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + 2x + 3x = 98 - 6 - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 6x = 90[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 90 \div 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 15[/tex]

So, tge required numbers are : 15, 16 and 17

Answer:

-22

Step-by-step explanation:

put the subtraction sign to the side

26 (Gretta's elevation)

-  4 (Hercules' elevation)

22

then re-add the subtraction sign (-22) then you have an answer

Please see the attached image for your answer. Hope this helps! If you can't read something please let me know.

Answer:

10.7a + (−6)

Step-by-step explanation:

Answer:

1,3,5,7,9,11,13,15,17,19

add them all together

= 100

Step-by-step explanation:

hope this works :)

Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.

Eva takes to fill an online order at her clothing boutique. = 6 minutes

If Eva and Briana fill an order together = 4 minutes

Briana will take minutes to fill an order alone at her clothing boutique = X minutes.

then the equation will be :

1/6 + 1/x = 1/4

1/x =  1/4 -  1/6

now solve equation by taking LCM

1/x = (6-4)/4x6

1/x = 2/24

1/x = 1/12

x = 12

so the value of x is 12

Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.

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The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.

What is a quadratic equation?

In algebra, a quadratic equation is any equation that can be rearranged in standard form as

ax² + b*x + c = 0

The figures a, b, and c are the portions of the equation and may be distinguished by calling them, independently, the quadratic measure, the direct measure, and the constant or free term.

The values of x that satisfy the equation are called results of the equation, and the roots or bottoms of the expression on its left-hand side.

A quadratic equation has at most two solutions.

Given,

Initial height h(0) = 3 ft

Initial upward velocity v(0) = 36 ft/sec

Given ball height after 't' seconds is h(t) = 3 + 36t - 16r²

for h= 19 ft

19 = 3 + 36 t - 16 r²

16 r² - 36 t + 16 = 0

4 r² - 9 t + 4 = 0

Quadratic equation for ax² + b*x + c = 0 is x = -b ±√b² - 4ac / 2a

By using the above formula we get

t = 9 ± √9² - 4*4*4 / 2*4

t = 9 ± √81 - 64 / 8

t = 9 ± √17 / 8

t = 9 + √17 / 8              t = 9 - √17 / 8

t = 9 + 0.5                    t = 9 - 0.5

t = 9.5                           t = 8.5

The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.

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Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Before beginning the problem, we have that the symbol # represents a pound, which has 16 ounces.

The remaining fillets weight 4 # 15 oz = 4 pounds + 15/16 of a pound. Hence, considering the cost of $2.74 per pound:

4 x 2.74 + 15/16 x 2.74 = $13.53.

The total value of the remaining fillets is of $13.53.

The price per pound is still the same, of $2.54.

The yield is of 4 pounds + 15/16 of a pound = 4.9375 pounds out of 7 + 6/16 = 7.375 pounds, hence the percentage is:

4.9375/7.375 x 100% = 66.95%.

The salmon’s yield percentage is of 66.95%.

Hence, for 6 + 14/16 = 6.875 pounds, the yield would be of:

0.6695 x 6.875 = 4.6 pounds.

You would expect to yield 4.6 pounds of boneless salmon fillet from the next salmon weighing 6 # 14 oz.

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Option a is correct. f(x) has an inverse function because its graph passes the horizontal line test.

An inverse function is a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

From the graph we can see that the horizontal lines intersect less than 2 points, this shows that the f(x) has an inverse.

From the graph, it gets to know.

Hence from the given graph we get to know that f(x) is the inverse function.

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Answer:

{-2/3, 10/3}

Step-by-step explanation:

Let's solve your equation step-by-step.

|3x−4|=6

Solve Absolute Value.

|3x−4|=6

We know either3x−4=6or3x−4=−6

3x−4=6(Possibility 1)

3x−4+4=6+4(Add 4 to both sides)

3x=10

3x/3 = 10/3

(Divide both sides by 3)

x=10/3

3x−4=−6(Possibility 2)

3x−4+4=−6+4(Add 4 to both sides)

3x=−2

3x/3 = −2/3

(Divide both sides by 3)

x= −2/3

The probability that a random bird chosen from among these is NOT a duck is 0.67

Given the total number of birds = 262

No of geese = 65

No of ducks = 84

No of robins = 113

We need to find the probability that a random bird chosen from among these is not a duck is

P ( not a duck ) = (total number of birds  - no of ducks) / total number of birds

                         =  262 - 84 / 262

                         =  178 / 262

                          = 0.67

The probability that a random bird chosen from among these is NOT a duck is 0.67.

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Answer:  Continuous at x = 3

The function is only discontinuous at x = 0 since it causes a division by zero error. Everywhere else the function is a continuous curve.