Step-by-step explanation:
The heaviest legal bowling ball weighs 16 pounds. The lightest weight you can usually find at most bowling alleys is six pounds.
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Steve weatherspoon, a super salesman contemplating retirement on his 50th birthday, decides to create a fund on an 11% basis that will enable him to withdraw 14,570 per year on June 30th, beginning in 2024 and continuing through 2027. To develop this fund, Steven intends to make equal contributions on June 30th of each of the years 2020 through 2023. How much must the balance of the fund equal on June 30th 2023 in order for Steve to satisfy his objective?
Based on the amount that Steve Weatherspoon wants to withdraw every year beginning in June 30, 2024, and the interest rate, the balance on June 30th 2023 should be $45,203.
What should the balance be in 2023?The fact that Steve Weatherspoon wants to be able to withdraw a particular amount every year, this makes this amount an annuity.
The value in 2023 would therefore be the present value of the annuity that will then accrue to the required amounts as the years go by.
The present value of an annuity is:
= Annuity amount per year x Present value interest factor of an annuity, 11%, 3 years between 2024 and 2027
Solving gives:
= 13,126.25 x 3.44371
= $45,203
In conclusion, the balance on the fund in 2023 should be $45,203 in order for Steve Weatherspoon to achieve his objectives.
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Screenshot below will hold the question.
The equation the completes the proof in step 6 is m<w + m<x = m<x + m<z
How to complete the proof?In step 4 of the proof, we have the following equation
m<w + m<x = m<y + m<z
In step 5, we have
m<x = m<y
When m<x = m<y is substituted to the equation in step 4, we have:
m<w + m<x = m<x + m<z
Hence, the equation the completes the proof in step 6 is m<w + m<x = m<x + m<z
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Which polygon does not belong with the others?
Manufacturers of tires report that car tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 51,500 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot.
Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage of the tire?
Yes, because a mean mileage of 51,500 or more occurred only 14 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
Yes, because a mean mileage of 51,500 or less occurred 186 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 51,500 or less occurred 186 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 51,500 or more occurred 14 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
There is convincing evidence the new type of tire tread improves mileage of the tire.
How to interpret the mean mileage?The given parameter is:
Average = 50000 miles
New average = 51500 miles
The dot plot is added as an attachment
From the dot plot, we can see that the mean value of 51500 or more occurred 14 times out of the 200 samples
So, the conclusion is that: (a) Yes, because a mean mileage of 51,500 or more occurred only 14 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
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Help me with this I need help asap!
Answer:
29.5
Step-by-step explanation:
[tex]UV=\frac{27+32}{2} \\ \\ UV=29.5[/tex]
Evaluate (f. g)(x) if f(x) = 2x² and g(x) = 3x - 2
Answer:
18x2 -24 x + 8
Step-by-step explanation:
( f o g) (x) = f ( g(x) ) = f( 3x-2) = 2( 3x-2)2 = 2( 9x2 - 12x + 4) = 18x2 -24 x + 8
Find the midpoint of the segment with the following endpoints.
(10, 3) and (2, 9)
. Find the perimeter of a regular pentagon with each side measuring 4.5 inches.
Answer: 22.5 inches
Step-by-step explanation:
the general formula for finding perimeter is [tex]p=s+s+s...[/tex]a pentagon contains 5 sides[tex]p=s+s+s+s+s[/tex]
note that this is a regular pentagon so it must contain 5 congruent sideseach side will be 4.5 inchesthe formula can be changed to [tex]5(s)[/tex] and solved:[tex]5(4.5 in)=p[/tex]
∴ 22.5 inches = perimeter of the pentagon
Find the missing side length in the image below 12 18 and 10
The missing length of the right triangle is 13.41 inches.
How to find the side of a right triangle?A right angle triangle has one of its angles as 90 degrees.
The side length of a right triangle can be found using Pythagoras theorem.
Therefore,
c² = a² + b²
where
c = hypotenusea and b are the other legs.Therefore,
x² = 18² - 12²
x² = 324 - 144
x² = 180
x = √180
x = 13.416407865
x = 13.41 inches
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Explain how to modify the graphs of f(x) and G(x) to graph the solution set to the following system of inequalities. How can at least solution set be identified?
Give f(x) a dotted boundary and shade it above.
Give g(x) a solid boundary and shade it above.
The solution set is the region that is in the shaded region of both graphs.
just need all answers to 19 asap please
Answer:
1&2)
GH = 28
FH = 56
XY = 7
XZ = 14
3-6) Acute, Obtuse, Acute, Right
7) Perimeter: 40 in. Area: 84 in^2
8) Perimeter: 42 m. Area: 84 m^2
9) Perimeter: 15.2 yd. Area: 14.44 yd^2
10) 1, 8, 27, 64, 125 These are the cubes of 1, 2, 3, 4, 5 so it's just the cube of the next number that was cubed before.
11) 128, 32, 8, 2, 1/2 Divide the previous number by 4.
12) 2, -6, 18, -54, 162 Multiply the previous number by -3
13-15) I'm sorry we didn't do those so I don't really know how that works sorry.
16) 3x - 14 = 34
3x = 48 Add 14 to each side (to isolate 3x)
x = 16 Divide by 3 both sides (to get x)
17) -4(x+3) = -28
x+3 = 7 divide by -4 on both sides (to get a step closer to solving for x and isolating x+3)
x = 4 subtract 3 from both sides (to get x (isolating x))
18) 43 - 9(x-7) = -x - 6
43 - 9x + 63 = -x - 6 distribute 9 to x and 7 (to expand)
106 - 9x = -x - 6 combine like terms (easier to deal with)
106 - 8x = -6 add x to both sides (so there's only x on one side)
112 - 8x = 0 add 6 to both sides (only one number left)
112 = 8x move -8x to the right side
x = 14 divide by 8 (to isolate x)
19) x = 29 degrees
20) x = 13 degrees
21) x = 9 degrees, y = 31 degrees
Step-by-step explanation:
4x = 5x-7
x = 7
GH = 5(7) - 7 = 35 - 7 = 28
FH = 4x + 5x - 7 = 4(7) + 28 = 28*2 = 56
3x - 5 = x + 3
x = 4
XY = 3(4) - 5 = 12 - 5 = 7
XZ = 7*2 = 14
Acute is < 90
Obtuse is > 90
Right is = 90
Straight is = 180
7) 2(6+14) = 2(20) = 40 in
6*14 = 84 in^2
8) 13+14+15 = 42 m
(12*14)/2 = 6*14 = 84 m^2
9) 3.8*4 = 15.2 yd
3.8^2 = 14.44 yd^2
19) 34 + 4x + 30 = 180
64 + 4x = 180
4x = 116
x = 29
20) 4x + 7x + 37 = 180
11x = 143
x = 13
21) 3y + 42 = 9x + 54
y + 14 = 3x + 18
y = 3x + 4
3y + 42 + 5x + 9x + 54 + 5x = 360
3y + 19x = 264
substitute y with 3x + 4
3(3x + 4) + 19x = 264
9x + 12 + 19x = 264
28x = 252
x = 9
so y = 3(9) + 4 = 27 + 4 = 31
the measure of the angels of a quadrilateral are in ratio 2:4:5:7 find the measure of each of it's angles
Answer:
Step-by-step explanation:
If they all exist in proportion to one another (READ: ratio) then multiplying each of the angles by the same number (here, some unknown "x" value) will maintain the proportionality. Since all the angles of a quadrilateral have to add up to equal 360, then
2x + 4x + 5x + 7x = 360 and
18x = 360. Divide both sides by 18 to get that
x = 20. That means that
2x = 2(20) = 40 and
4x = 4(20) = 80 and
5x = 5(20) = 100 and
7x = 7(20) = 140. Adding all of those up:
40 + 80 + 100 + 140 = 360
Answer:
40,80,100,140
Step-by-step explanation:
Let the ratio 2:4:5:7 angles be 2x, 4x, 5x, 7x
Now
2x + 4x + 5x + 7x=360 degrees
18x = 360 degrees
x =360/18
x=20
2x=2 *20=40
4x=4 *20=80
5x=5 *20=100
7x=7* 20=140
Write 636,000 in scientific notation.
HELP ME PLEASE
Vanessa knows that about 20% of the students in her school are bilingual. She wants to estimate the probability that if 3 students were randomly selected, all 3 of them would be bilingual. To do so, she will use a spinner with 5 equally sized sections labeled as either "bilingual" or "monolingual". She will spin the spinner 3 times, record the results, and repeat the process 50 times.
How many of the 5 sections should she label "bilingual"?
How many of the 5 sections should she label "monolingual"?
Answer:
1 section should be labelled "bilingual".
4 sections should be labelled "monolingual".
Step-by-step explanation:
If 20% of students in the school are bilingual, then 80% of students in the school are monolingual, since 100% - 20% = 80%.
If the spinner is to be divided into 5 equally sized sections, with each section labeled as "bilingual" or "monolingual" to represent the corresponding proportion of students in the school, then:
Bilingual
20% of 5
= 20/100 × 5
= 100/100
= 1 section
Monolingual
80% of 5
= 80/100 × 5
= 400/100
= 4 sections
Therefore:
1 section should be labelled "bilingual".4 sections should be labelled "monolingual".The Two sets A and B are said to be disjoint sets if A n B=_____
The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
What does it mean for two sets to be disjoint?Disjoint sets are a pair of sets that do not share any elements. For instance, sets A=2,3 and B=4,5 are not connected sets.When two sets don't share elements, they are considered disjoint sets. In other words, the null set will result if we find the intersection of two sets. The process is straightforward; two sets are given in this procedure.When using a disjoint set union, it is possible to add new sets, combine existing sets, and check whether two sets of elements are the same in almost real-time.The Two sets, A and B, are said to be disjoint sets if A n B=ϕ
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Julio wants to calculate 200,000 × 300,000. When he used his calculator to multiply, it showed the result below:
6E+10
Write the number shown on the calculator display in standard form.
The number shown on the calculator display can be written in standard form as 6 x 10¹⁰.
Product of 200,000 and 300,000The product of 200,000 and 300,000 is calculated as follows;
200,000 × 300,000 = 6E+10
What is standard form?Standard form is a mathematical way or a standard way of presenting numbers as a mathematical expression.
It presents numbers in the simplest form.
Product of 200,000 and 300,000 in standard form200,000 × 300,000 = 6 x 10¹⁰
Thus, the number shown on the calculator display can be written in standard form as 6 x 10¹⁰.
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(4x³-12x +11) + (2x - 2)
Graph the following conditions. {(x, y): x + 2y > 6}
See attachment for the graph of the inequality expression x + 2y > 6
How to graph the conditions?The condition is given as:
{(x, y): x + 2y > 6}
This means that
x + 2y > 6
The above is an inequality expression, where the variables are x and y
So, we simply plot the graph of the inequality expression x + 2y > 6
See attachment for the graph of the inequality expression x + 2y > 6
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Can u guys please give me the correct answe
Answer:
35
Step-by-step explanation:
Since the two sides are equal in a parallelogram angle B = y ,so we have angle to be equal to 145°
We sum both angles and divide from
360° - [145° +145°]
360° - 290° = 70
Since the left sides( X And Z) are equal then we divide what we got into 2
70 ÷ 2 = 35
therefore angle X equals 35
What is the component form of the vector that translates the top house figure to the
bottom house figure?
The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).
What is the vector component form?The component form of a vector is known to be depicted as < x, y >.
Note that:
x - tells the distance or how far to the right or left, a vector is known or seen to be going.
y - tells the distance or how far to the upper part or downward a vector is known or seen to be going.
From the question and looking at the image attached, we were able to obtain (-4,4) and (2, 0)
So:
⇒ (-4,4) --------(-4+6)(4-4)-------(2,0)
⇒ (6,-4)
Hence, The component form of the vector that translates the top house figure to the bottom house figure is (6, -4).
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(-4,2) (5,0) midpoint
Answer:
[tex]M = (0.5, 1)[/tex]
Step-by-step explanation:
The midpoint can be found using the formula: [tex]x, y = (\frac{x_2+x_1}{2}, \frac{y_2 + y_1}{2})[/tex]
So plugging in the values we get: [tex]M = (\frac{-4+5}{2}, \frac{2+0}{2})\\M = (\frac{1}{2}, \frac{2}{2})\\M = (0.5, 1)[/tex]
Answer: [tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]
Step-by-step explanation:
Given information
(x₁, y₁) = (-4, 2)
(x₂, y₂) = (5, 0)
Given formula for midpoint
[tex]Midpoint~=~(\frac{x_1~+~x_2}{2} ,~\frac{y_1~+~y_2}{2} )[/tex]
Substitute values into the formula
[tex]Midpoint~=~(\frac{-4~+~5}{2} ,~\frac{2~+~0}{2} )[/tex]
Simplify by addition
[tex]Midpoint~=~(\frac{1}{2} ,~\frac{2}{2} )[/tex]
Simplify fractions if necessary
[tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Evaluate this exponential expression.
OA. 19
OB. 63
OC. 66
OD. 207
6 (4+2)²-32
Answer: 184
(I am not sure if I have misunderstood the question, but the final answer I got was 184, which wasn't any one of the choices. I was wrong in understanding, please let me know and I will modify my answer)
Step-by-step explanation:
Given expression
6 (4 + 2)² - 32
Simplify values in the parenthesis
6 (6)² - 32
Simplify exponents
6 × 36 - 32
Simplify multiplication
216 - 32
Simplify subtraction
[tex]\Large\boxed{184}[/tex]
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Please let me know if you have any questions
A group of people were asked which of three ice cream flavors they prefer. The results are shown in the table.
Ages Vanilla Strawberry Chocolate
20 years and younger 8 10 6
Over 20 years 8 6 12
What is the probability of a person being over 20 years old and preferring vanilla ice cream?
8%
13%
16%
26%
Answer: 8/50 = 16%
Step-by-step explanation:
Find the length of the a of a right triangle b=21.5 inches and the hypotenuse c =31.9.use the calculator to estimate the square root to one decimal place
The length of the leg a is approximately?
Answer:
Step-by-step explanation:
a² + b² = c²
a² + (21.5)² = (31.9)²
a² + 462.25 = 1017.61
a² = 555.36
a = 23.6
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
The required steps are
2x^2 + 12x – 3 = 0.
2x2 + 12x = 3
2(x^2+6x) = 3
2[(x+3)^2 - 9] = 3
Completing the square methodQuadratic equations are equations that has a leading degree of 2
Given the equation below;
2x^2 + 12x – 3 = 0.
Add 3 to both sides
2x2 + 12x = 3
Factor out 2
2(x^2+6x) = 3
Complete the square
2(x^2+6x+3^2-3^2) = 3
2[(x+3)^2 - 9] = 3
This gives the required steps to solve the equation
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Ashlee sells lunches for $7.00 and drinks for $2.25. One busy Saturday, Ashlee sold $440.00 worth of lunches and drinks. Which equation represents the relation between the number of lunches sold, x, the number of drinks sold, y, and the amount in dollars that Ashlee sold that day?
Group of answer choices
Answer:
7x + 2.25y = 440
Step-by-step explanation:
Ashlee sells lunches for $7.00 and drinks for $2.25.
One busy Saturday, Ashlee sold $440.00 worth of lunches and drinks.
The number of lunches sold is x.
The number of drinks sold is y.
The appropriate equation will be:
= (7 × x) + (2.25 × y)
7x + 2.25y = 440
George has 50,000in wage income ,20,000 in gambling winning .10,000 in alimony income and 5,000 in divided income the amount of George income that is subject to withholding is
The amount of George's income that is subject to withholding is $75,000, which excludes the alimony income.
What is alimony income?Alimony income represents the amount received from a spouse or a former spouse under a divorce or separation instrument.
What are the incomes subject to withholding?The incomes subject to withholding include the following:
Regular CommissionsVacation payReimbursementsOther expense allowances PensionsBonusesDividendsGambling winnings.Data and Calculations:Wages income = $50,000
Gambling winning = $20,000
Alimony income = $10,000
Dividend income = $5,000
Income subject to withholding = $75,000 ($20,000 + $20,000 + $5,000)
Thus, George's income that is subject to withholding is $75,000, excluding the alimony income.
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A pack of soil weighs 43 lbs. Each plant pot requires just 12 lbs of soil.
Calculate how many plant pots can be filled.
What is the probability that the top-three finishers in the contest will
all be seniors?
Type in the correct answer in each box. Use numerals instead of
words. If necessary, round your answers to the nearest tenth.
Answer: Just guessing, try.. or dont.
Step-by-step explanation:
There are 3 seniors. To make up 100% we would have to do 33.33%. I would say that the probabilty is around 33.33, and don't know the different orders possible.
Solve for x. You must show all of your work to receive credit.
Answer:
x = 6
Step-by-step explanation: