Steven wants to buy a couch that costs $475. He has already saved $120. He plans to save $25 a week.
Enter a function to represent the amount Steven will have saved in x weeks. Will he have enough to buy
the couch in 10 weeks? Complete the explanation.

Answer:

Price decresed to 124.00

Step-by-step explanation:

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

Step-by-step explanation:

Arithmetic sequence

First term a = 13

Common difference = 2nd term - first term

                                 = 22 - 13

                             d = 9

\(a_{n}= a + (n-1)d\\\\a_{7}= 13 + 6*9\)

   = 13 + 54

  = 67

Sum of 7 terms = \(\frac{n}{2}(2a + (n-1)d)\\\\\)

                         = \(\frac{7}{2}(2*13+6*9)\\\)

                         =\(\frac{7}{2}(26+54)\\\)

                          = \(\frac{7}{2}*80\\\)

                         = 7 *40

                          = 280

Answer:

280

Step-by-step explanation:

the 7th number is

Answer:

y = 2x - 3

2y = x - 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

To get the y values all you need to do is substitute the x value in the equation y=-2/3x+7.

For example:

y=-2/3(-6)=7

-2/3x6=-4

-4+7=3

(-6,3)

You can double check your work by filling the x and y coordinates in the equation and when solved if it it true you know you were correct.

To get the x value, you need to fill in the y in the equation y=-2/3x+7

for example:

5=-2/3x+7

-2=-2/3x

3=x

(3,5)

y=-2/3x+7

y=-2/3(15)+7

y=-10+7

y=-3

(15,-3)

y=-2/3x+7

15=-2/3x+7

8=-2/3x

-12=x

(-12,15)

Work done lifting the bucket and rope to the top of the building is 4005.75 Joules

To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ.

Initially bucket hold = 25kg. Sand

Sand leaks 0.1 kgs each meter it is lifted

At height x meter bucket hold = (25 - 0.1x) kg of sand

Length of rope = 15 meter

density of rope = 0.4kg / meter

weight of rope = 15 (0.4) = 6kg.

At height x meter, weight of rope = (6 - 0.4x)

Total weight at height x meter = (25-0.1x) + (6-0.4x)

                                                   = (31 - 0.5x) kg

force = (31-0.5x) g Newtons. = [(31-0.5x) 9.8] Newton

Work = force × displacement

\(Work= \int_{0}^{15}9.8(31-0.5x)dx\)

          \(=9.8[31x-0.5 \frac{x^2}{2} ]_{0}^{15}\)

          \(=9.8[31(15)-0.25(15)^2]-0\)

          \(=4005.75 joules\)

Hence, work done 4005.75 Joules

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Answer:

D=360_180÷9

D=360_20

D=340

Answer:

Y(2)= 2120+ 48= 2168

Step-by-step explanation:

The given equation is

Yt= 2120 - 620 Qtr 1 t -1320 Qtr 2 t + 290 Q tr3 t + 24 t

Taking the quarter 1 , 2 and 3 to be dummy variable the predicted sales for the 4th qtr are

Yt= 2120 - 620 Qtr 1(0) -1320 Qtr 2(0) + 290 Q tr3 (0)  + 24 (1)

Y(1)= 2120 + 24 = 2144   ( for year =1)

Y(2)= 2120+ 48= 2168    ( for year =2)

Y(3)= 2120 + 72= 2192   ( for year =3)

where t is the number of years.

So for the next year the fourth quarter sales are predicted to be 2168.

Answer: 2 286/624

Step-by-step explanation:

96 * 16= 1536

125* 5= 625  

2 286/ 625

Answer:

Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number. Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.

Step-by-step explanation:

455,329,950 lie between 455,329,900 and 455,330,000

To round 455,329,950 to the closest hundred, we apply the rule to round the number with algarism 5. This rule determine that we must round the number to the closest even algarism in the place of the significant digit.

In this case, we must round 455,329,950 to 455,330,000.

Answer: The height of the pyramid is approximately 87.58 units.

Step-by-step explanation:

Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:

Now, let's use the given area and solve it for x:

Since the "path" already has fence, the amount of fence needed is 2x:

Answer:

5, 3, 0, 3 are all the ranges! Hope this helps

Step-by-step explanation:

Ranges are on the right, domains are on the left

Answer:

300% percent of the people are absent...

Step-by-step explanation:

Answer:

4\(\frac{5}{12}\) or \(\frac{53}{12}\)

Step-by-step explanation:

I hope this helps!

Answer:

b or c i think

Step-by-step explanation:

not for sure just a guess

1. In a rhombus, if DK = 8, then KL = DK = 8, 2. a. AD = AB = 15, b.  DC = AB = 15, c.  m∠BAD= 66°,  m∠ADC= 33°.

A rhombus is a four-sided polygon with all sides of equal length. It is also known as a diamond or a lozenge. It is a special case of a parallelogram, where opposite sides are parallel and diagonals bisect each other at right angles. In a rhombus, all angles are equal, and the opposite sides are parallel and congruent. The diagonals of a rhombus intersect at a 90-degree angle, and they bisect each other. The area of a rhombus can be calculated as half the product of its diagonals. The perimeter of a rhombus is four times the length of its sides. Rhombuses can be found in various contexts, such as in geometric shapes, logos, and patterns.

1. In a rhombus, all sides are equal. So, if DK = 8, then KL = DK = 8.

2. In a rhombus, opposite angles are equal. So, m<ADC = m<ABC = 114°.

a. In a rhombus, all sides are equal. So, AD = AB = 15.

b. In a rhombus, all sides are equal. So, DC = AB = 15.

c. The sum of angles in a rhombus is 360°. So, m∠BAD = (360 - 2*114)/2 = 66°.

d. In a rhombus, opposite angles are equal. So, m∠ABD = m∠DCB. Also, m∠ABD + m∠DCB = 180°. Therefore, m∠ADC = (180 - 114)/2 = 33°.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)

\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)

The total price of the vehicle would be $18,192.88.

The total deferred price of the car would be $11,191.60.

The length of the financing agreement is 68 months .

The total deferred price after the payments was $19,601.84.

The monthly payments would be $516.92.

Subtotal = Base price + Options + Destination charges

Subtotal = $14,500 + $982 + $592 = $16,074

Dealer preparation = 5% of subtotal

Dealer preparation = 0.05 x $16,074 = $803.70

Sales tax = 7% of subtotal

Sales tax = 0.07 x $16,074 = $1,125.18

Total price = Subtotal + Dealer preparation + Sales tax + Tag fee + Title fee

Total price = $16,074 + $803.70 + $1,125.18 + $145 + $45 = $18,192.88

Tax = 8% of selling price = 0.08 x $8,850 = $708

Tag fee = $130

Title fee = $35

Total amount financed = Amount financed + Tax + Tag fee + Title fee = $7,350 + $708 + $130 + $35 = $8,223

Annual interest rate = 9.5%

Number of years financed = 3

Total finance charges = $8,223 x 0.095 x 3 = $2,341.595

Total financed amount = $8,223 + $2,341.595 = $10,564.595

Monthly payments = Total financed amount / (Number of years financed x 12 months) = $10,564.595 / (3 x 12) = $293.4615

Total deferred price = Selling price + Total finance charges = $8,850 + $2,341.595 = $11,191.595

Total deferred price = $28,000

Down payment = $2,100

Total amount financed = Total deferred price - Down payment = $28,000 - $2,100 = $25,900

Monthly payments = $380

Number of months = Total amount financed / Monthly payments = $25,900 / $380 = 68.16

The financing agreement is approximately 68 months long.

Sticker price = $19,200

Discount = 6% of sticker price = 0.06 x $19,200 = $1,152

Selling price = Sticker price - Discount = $19,200 - $1,152 = $18,048

Sales tax = 8% of selling price = 0.08 x $18,048 = $1,443.84

Total price = Selling price + Sales tax + Tag fee + Title fee = $18,048 + $1,443.84 + $65 + $45 = $19,601.84

Using the formula for monthly payments on a loan:

P = (PV x r x (1 + r)^ n) / ((1 + r) ^ n - 1)

= ($26,515.80 x 0.005265 x (1 + 0.005265) ^ 60 ) / ((1 + 0.005265) ^ 60 - 1) = $516.92

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Answer:

i hope its readable lol-

Answer:

D. There is more variation in height at 24 months. The box length is​ longer, indicating a larger interquartile range and greater spread in the data

Step-by-step explanation:

One easy way we can easily tell about the spread and variation data sets is by considering the length of the box in the box plot.

The length of a box plot represents the interquartile range of a data set. The longer the box length, the more the variation and spread there is in the data.

Therefore, considering the diagram of the box plots attached below, the box length for length of boys at 24months is longer than that of the box length of heights of boys at 12 months.

The longer box lengths for heights of boys at 24 months indicates a larger interquartile range compared to that of heights of boys at 12 months. This larger interquartile range implies that, there is more variation in heights at 24 months.

Therefore, the correct option is "D. There is more variation in height at 24 months. The box length is​ longer, indicating a larger interquartile range and greater spread in the data."

Answer:

120 + 10x

or

10(12 + x)

Step-by-step explanation:

Answer:

Step-by-step explanation:

pi*r^2=area

1*1=1

1*3.14=3.14

the area is pi itself

Answer:

90% confidence interval for the difference between the two population means

( -23.4166 , -6.5834)

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 100

Given mean of the first sample x₁⁻ = 178

Standard deviation of the sample S₁ = 35

Given second sample size n₂= 100

Given mean of the second sample x₂⁻ = 193

Standard deviation of the sample S₂ = 37

Step(ii):-

Standard error of two population means

        \(se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }\)

       \(se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }\)

        \(se(x^{-} _{1} -x^{-} _{2} ) = 5.093\)

Degrees of freedom

ν  = n₁ +n₂ -2 = 100 +100 -2 = 198

t₀.₁₀ = 1.6526

Step(iii):-

90% confidence interval for the difference between the two population means

\((x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})\)

(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)

(-15-8.4166 , -15 + 8.4166)

( -23.4166 , -6.5834)

Answer:

A) at the Venus De Milo statue

Step-by-step explanation:

do it

Jake and Summer agreed to meet in this specific part of the museum in the story Teen detectives:

At the Venus De Milo statue

This is a reading comprehension activity about the story Teen detectives, which follows the adventures of Jake and Summer.

In reading comprehension exercises, you have to read the text or story carefully, then read the exercise's instructions and finally select the key words that can help you understand the whole story better.

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Answer:

Step-by-step explanation:

This problem is on the mensuration of solid shapes, an oblique cylinder.

the expression for the volume of an oblique cylinder is given as

\(volume= \pi r^2h\)

Given data

radius r= 5

height h= 12, and

slant length of 13.

Substituting the given data into the expression we can solve for the volume below

\(volume= \pi* 5^2*12\\\ volume= \pi*25*12\\\ volume= \pi*300\\\ volume= 300\pi\)

Answer:

300

Step-by-step explanation:

11. Angle KEF = 40°, Angle KEJ = 50°

12. Angle HEF = 115°, Angle KED = 140°

13. Angle JEF = 90°, Angle KEF = 90°

14.   Angle DEF = 180°

The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.

11.  Acute angles: Those angles are less than 90 degree angles.

     Angle KEF = 40°

     Angle KEJ = 50°

     Angle KEH = 75°

     Angle JEH = 25°

     Angle HED = 65°

12. Obtuse angles: Those angles are more than 90 degree angles.

     Angle HEF = 115°

     Angle KED = 140°

13. Right angle: Those angles are 90 degree angle.

     Angle JEF = 90°

     Angle KEF = 90°

14. Straight angle: Those angles make 180 degree angle.

     Angle DEF = 180°

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