The three consecutive integers according to the expression will be 6, 8, 10
In the given question, there is an expression stated that tells the condition for a sequence in which a number is represented by 'n'. The expression is the sum of three even integers whose sum is equal to four times the smallest of numbers.
The expression is n + (n + 2) + (n + 4) = 4n. We have to find out the values for each of the numbers.
Here, First Number = n
Second number = (n + 2)
Third Number = (n + 4)
Now, We will calculate the given expression to find out the value of n.
=> n + (n + 2) + (n + 4) = 4n
=> 3n + 6 = 4n
=> n = 6
We get the smallest number n = 6 which is the first number, the second number is 8, and the third number is 10.
Hence, the numbers are 6, 8, and 10.
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Ingrid hit a golf ball. the height of the golf ball (in meters above the ground) t seconds after being hit is modeled by h(t)=-5t²+30tIngrid wants to know when the ball reached its highest point 1) rewrite the function in a different form (factored or vertex) where the awnser appears as a number in the equationh(t)=___2) How many seconds after being hit does the ball reach its highest point?____ seconds
Write the equation in vertex form to find the maximum height, as well as the time when the maximum height is reached.
The vertex form of a quadratic equation is:
[tex]y=a(x-h)+k[/tex]Where (h,k) is the vertex of the parabola, k is the maximum or minimum value and h is the value of x where that maximum or minimum is reached.
To write h in vertex form, complete the square:
[tex]\begin{gathered} h(t)=-5t^2+30t \\ =-5(t^2-6t) \\ =-5(t^2-6t+9-9) \\ =-5((t-3)^2-9) \\ =-5(t-3)^2-5(-9) \\ =-5(t-3)^2+45 \end{gathered}[/tex]We can see that in this case, the vertex is (3,45).
Therefore:
1)
[tex]h(t)=-5(t-3)^2+45[/tex]2)
The ball reaches the maximum height 3 seconds after being hit.
Elinor wanted to order an 18 inch hoagie, which cost $7.99. The sandwich shop is out of 18 inch buns. They only have 12 inch buns.
The price of 12 inch bun purchased by Elinor is $5.32.
What is defined as the method of unitary?The unitary method determines the value of a unit and afterwards the value of such a necessary number of units. The value of a unit amount is determined first in the unitary method before calculating the value of many other units. It comes in two varieties.Variation in DirectVariation in the inverseFor the given question;
Elinor wanted to have a bun.
The cost of 18 inch hoagie bun is $7.99.
As there is only 12 inch bun present, the price of 12 inch bun is calculated by unitary method.
The price can be written as;
18 inch -------> $7.99
For 1 inch bun, divide both side by 18.
18/18 inch -------> $7.99/18
1 inch -------> $7.99/18
For 12 inch, multiply each side by 12.
12 inch -------> $7.99×12/18
12 inch -------> $5.32
Thus, the price of 12 inch bun is $5.32.
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Target's sells casual sandals for $12 and dress sandals for $22. Total sandals sales were $2,300, and customers bought twice as many casual sandals as dress sandals. How many dress sandals did customers buy? (Hint: Let D = the number of dress sandals.)
Answer:
50 dress sandals
Step-by-step explanation:
Let D = number of dress sandals and C = number of casual sandals
Customers bought twice as many casual sandals as dress sandals. In algebraic form this would be
S = 2D (number of casual sandals = 2 times number of dress sandals)
Since casual sandals sell for $12 each and dress sandals for $22 each, the total sales for S casual and D dress sandals
= 12S + 22D = 2300 (given)
Substitute S = 2D into the above equation to get
12 (2D) + 22D = 2300
24D + 22D = 2300
46D = 2300
D = 2300/46 = 0
Answer: Customers bought 50 dress sandals
You purchase six municipal bonds on the first of the year. The current market value price is 103. The commission charge is $5 per bond. What is the cost of the purchasing these bonds?
a.
$6210
b.
$633
c.
$648
d.
$3090
Answer:
C
Step-by-step explanation:
(103 + 5) * 6 = 648
Ratio
$1.25
1 slice
$10.00
8 slices
1 book
5 days
25 miles
1 gallon
Unit rate
Not a unit rate
Answer:
Step-by-step explanation:
$1.25 for 1 slice is the unit rate because a unit rate is the measure of a single unit, which in this case is 1 slice.
What is the rate of return when 25 shares of Stock A, purchased for $30/share, are sold for $825? The commission on the sale is $6. Rate of Return = [?] %
Given:
The rate of return when 25 shares of Stock
A. purchased for $30/share, are sold for $825. The commission on the sale is $6.
Required:
What is the rate of return?
Explanation:
First step is to find the shares of stock price:
Shares of stock price=25 shares×$30/share
Shares of stock price= $750
Second step is to calculate the total sold price:
Total sold price= $825+$6
Total sold price= $831
Third step is to calculate the Rate of return:
[tex]\begin{gathered} \text{ Rate if return }=\frac{831-750}{750}\times100 \\ \text{ Rate if return }=\frac{81}{750}\times100 \\ \text{ Rate of return }=10.8\% \end{gathered}[/tex]Answer:
Rate of return is 10.8%
A manager at a shipping company will purchase boxes in the shape of a right rectangle prisms he wants the volume of each box to be exactly 98 cubic ftwhich figure shows a box with the dimensions in feet that the manager will purchase
We have that the general equation for the volume of a rectangle prism is:
[tex]V=lwh[/tex]where l represents the length of the base, w represents the width of the base and h represents the height of the prism.
Since we need that the volume be equal to 98ft³, we have that the measures for the prism are:
[tex]V=(7)(3.5)(4)=98ft³[/tex]therefore, the prism would look like this:}
A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.Part A: How many miles did the hiker travel on the first day? Round your answer to the nearest mile and show all necessary math work. (4 points)Part B: What is the equation for Sn? Show all necessary math work. (3 points)Part C: If this pattern continues, what is the total number of miles the hiker will travel in 10 days? Round your answer to the hundredths place and show all necessary math work. (3 points)
Answer with explanation: A hiker has increased his distanced covered by 10% each day since the start, the total distance covered at the end of the 7th day is 75.897mile:
(A) The number of miles on the first day:
[tex]\begin{gathered} \text{let x be the distance covered on first day:} \\ x,1.1x,1.21x,1.331x,\ldots. \\ \text{ This is a Geomatric sequence:} \\ S_n=\frac{a(r^n-1)}{r-1} \\ a=x \\ r=\frac{1.1x}{x}=1.1 \\ r=1.1 \\ n=7 \\ S_n=\frac{x((1.1)^7-1)}{1.1-1}\Rightarrow(0) \end{gathered}[/tex]Substituting the total miles covered on the 7th day in equation(0) gives:
[tex]\begin{gathered} 75.897=\frac{x((1.1)^7-1)}{1.1-1} \\ 7.5897=0.9487171x \\ x=7.9999612107761101807904590314647 \\ x\approx7.9999mi \end{gathered}[/tex]Therefore on the first day, the hiker covered about 7.99 miles:
(B) The equation for the S:
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow(1) \end{gathered}[/tex]The equation (1) gives the number of miles hiked on the nth day.
(C) miles covered on 10th day:
The number of miles covered on the 10th day is calculated using the equation(1) as follows:
[tex]\begin{gathered} S_n=\frac{7.99((1.1)^n-1)}{1.1-1}\Rightarrow n=10 \\ S_{10}=\frac{7.99((1.1)^{10}-1)}{1.1-1} \\ S_{10}=127.340mi \end{gathered}[/tex]The number of miles covered on the 10th day is 127.340miles.
About the formula used:
[tex]\begin{gathered} S_n=\frac{a-ar^n}{1-r}\Rightarrow\text{ Your formula} \\ \text{Multiply by:} \\ \frac{(-1)}{(-1)} \\ \therefore\Rightarrow \\ S_n=\frac{(-1)}{(-1)}\times\frac{(a-ar^n)}{(1-r)}=\frac{(-1)\cdot(a-ar^n)}{(-1)\cdot(1-r)}=\frac{-a+ar^n}{-1+r}=\frac{ar^n-a}{r-1} \\ S_n=\frac{ar^n-a}{r-1}=\frac{a(r^n-1)}{r-1} \\ S_n=\frac{a(r^n-1)}{r-1}\Rightarrow\text{ My formula} \end{gathered}[/tex]In conclusion, the formula used is the same as the one that was required to be used.
Please help again please help me
Answer:
-0.5,-1/5,0.7,3/4 its correct
Answer:
-0.5, -1/5, 0.7, 3/4
Step-by-step explanation:
We can convert the fractions into decimals.
-1/5 = -0.2
3/4 = 0.75
-0.5 is the least, then -1/5, then 0.7, and lastly 3/4.
Hope this helps!
P.S, Can I get a brainliest if this is right? Thanks!
Amber rolls a 6-sided die. On her first roll, she gets a "4". She rolls again.(a) What is the probability that the second roll is also a "4".P(4 | 4) =(b) What is the probability that the second roll is a "1".P(1l4)
The probability of getting a 4 again means is given by the product of the probabilities to obtain 4 twice (because in this case we have independent events)
(a) P(4I4) = P(4)*P(4) = (1/6)(1/6) = 1/36
(b) P(1l4) = P(1)*P(4) = (1/6)(1/6) = 1/36
In the previous calculations we have considered that the probability for getting any number is the same and it is 1/6.
Bridget sold a total of $135 at her yard sale. If she sold a lamp for $35.50 more than the cost of everything else, what was the cost of the lamp and everything else.
The cost of lamp and everything else will be equal to $85.25 and $49.75 respectively.
This question can be solved by converting it into the form of linear equation. A linear equation can be expressed in the form of y = ax + b where a, b are coefficients and x, and y are independent and dependent variables. We know the total sale which is equal to $135. Let us assume the cost of everything else as x. Now, the cost of lamps is $35.50 more than cost of everything else that is equal to x + 35.50. Now, the linear equation will be written as
135 = x + (x + 35.50)
135 = 2x + 35.50
=> 2x = 99.5
=> x = $49.75 which is the cost of everything else and cost of lamp = x + 35.50 = $85.25.
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Write the equation of the line with a slope of -3 that passes through (-5,20)
SUBSTITUTE THE KNOWNS IN THE GIVEN GENERAL EQUATION BELOW AND SIMPLIFY TO GET c
[tex]y = mx + c \\ 20 = - 3( - 5) + c \\ 20 = 15 + c \\ c = 20 - 15 \\ c = 5[/tex]
Meaning
[tex]y = - 3x + 5[/tex]
IS THE EQUATION
find the rate of change of its elevation when x=22
To find the rate of change of its elevation we can derive the position function:
[tex]y=-\frac{1}{110}x^2+127[/tex][tex]y^{\prime}=\frac{d(y)}{dx}=d(-\frac{1}{110}x^2+127)/d(x)[/tex][tex]y^{\prime}=\frac{-1}{55}x[/tex]The rate of change of its elvation when x=22 is
[tex]\frac{-1}{55}\cdot22=\frac{-22}{55}=\frac{-2}{5}=-0.4[/tex]That represents the slope of the tangent line to the function at x=22.
3] If the p.d.f., of the random variable X is given byf(x)= K sqrt x &0 1)(c) P(|X| < 3)(d) E(2X - 2)(e) V(3X)
aIn a class of students, the following data table summarizes how many students passeda test and complete the homework due the day of the test. What is the probability thata student who passed the test did not complete the homework?Passed the test Failed the testCompleted the homework112.2Did not complete the homework3N
According to the given table, the number of students that passed the test and did not complete the homework is
[tex]3.[/tex]Also, from the table, we get that the total number of students that passed the test is
[tex]11+3=14.[/tex]Therefore, the probability that a student that passed the test did not complete the homework is:
[tex]\frac{3}{14}\text{.}[/tex]Answer:
[tex]\frac{3}{14}\text{.}[/tex]What is the domain and range? What does it mean in terms of the graph?
The domain of the graph is [0,14] and the range of the graph is [0, 7]
In this question, we have been given a graph of height of a falling object.
In this graph, x-axis represents the time in seconds and y-axis represents the height in meters.
We know that, the domain of a graph consists of all the input values which are on the x-axis and the range is the set of possible output values, which are shown on the y-axis.
In this graph we can see that the input (time) takes the values between [0, 14] and the output (height) has values in the interval [0, 7]
Therefore, the domain of the graph is [0,14] and the range of the graph is [0, 7]
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For what value of x will 3x + 4 = x - 6 be a true statement?
A x = -5
В. x = -5/2
C x = -1
D x = - 1/2
Answer:
A
Step-by-step explanation:
3x + 4 = x - 6 ( subtract x from both sides )
2x + 4 = - 6 ( subtract 4 from both sides )
2x = - 10 ( divide both sides by 2 )
x = - 5
Answer:x 1= x. Examples: 41=4. 5)
Step-by-step explanation:
If 2(x-8)= - 4x+2 , then x=
A) -7
B) -5
C) 3
D) 9
Answer:
C) 3
Step-by-step explanation:
2(x - 8) = -4x + 2
2x - 16 = -4x + 2
6x - 16 = 2
6x = 18
x = 3
Find the distance between the two points rounding to the nearest tenth (if necessary). (5,-8) and (-3,-1)
Answer: [tex]\sqrt{113}[/tex]
Step-by-step explanation:
You use the Pythagorean Theorem for problems like this.
1. First you figure out the distance between the points.
2. As seen in the picture, the yellow line is 7 units long and the blue line is 8 units long.
3. From here you substitute the numbers into the Pythagorean Theorem. [tex]7^{2} +8^{2} =c^2[/tex]
4. Now solve. This gives you [tex]\sqrt{113}[/tex]
what is the daily recommended amount of vitamin A if 15% is 150 mcg?
If x is the daily amount of Vitamin A and we know that 15% of x is 150 mcg, we can calculate x as:
[tex]\begin{gathered} 15\%\cdot x=\frac{15}{100}x=0.15x=150 \\ x=\frac{150}{0.15} \\ x=1000 \end{gathered}[/tex]Answer: the recommended daily amount of Vitamin A is 1000 mcg.
The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of error
of 13%. What is the maximum the company can expect for returned items?
O $3268.20
$3668.30
O$4425.60
O $4902.30
Using proportions, it is found that the maximum the company can expect for returned items is of:
$4,616.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division along with the unit rates in the context of this problem.
The lost amount to returns each day is of 15% of 27235, and this amount is calculated as follows:
0.15 x 27235 = $4,085.25
(the decimal equivalent of the percentage is multiplied by the original amount to find the equivalent amount).
The margin of error is of 13%, hence this amount can still be increased by 113, that is, multiplied by 1.13, hence:
4085.25 x 1.13 = $4,616.
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Answer:
The answer is D $4902.30
Step-by-step explanation:
Kathy Runde, age 66 and retired, receives a $20,000 partial distribution from her 401(k) plan. The plan does not pay out an annuity. Immediately before the distribution, her account balance is $50,000, including $10,000 in nondeductible contributions. How much of the $20,000 distribution must Kathy include in gross income?
The whole twenty thousand dollars that were distributed has to be accounted for as part of the gross revenue.
This is further explained below.
What is gross income?Generally, A person's or a household's gross income is the whole amount of money earned before any deductions or taxes are taken out of that income. This includes all wages, salaries, profits, interest payments, rentals, and other types of earnings.
Because it is treated as regular income, the amount that was withdrawn is subject to taxation at the same rate as ordinary income under the federal income tax system.
If, on the other hand, Kathy makes the decision to convert her 401(k) to a Roth 401(k), then any money she takes out of the account will not be subject to taxes.
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You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $3500 per month. You have access to an account that pays an APR of 4.8% compounded monthly. This requires a nest egg of $610,823.48.
What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)
The monthly deposit that is required to achieve the desired monthly yield at retirement is $1,056.71.
What is the monthly deposit?An annuity is a series of payment that is made over a period of time. The annuity in this question would last for 25 years. When an investment is compounded monthly, it means that the investment would grow at an exponential rate once in a month.
The formula that would be used to determine the monthly payment is:
Monthly payment = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = monthly interest rate = 4.8% / 12 = 0.4%n = number of periods = number of compounding x number of years: 12 x 25 = 300$610,823.48 ÷ [{(1.004^300) - 1} / 0.004] = $1,056.71
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What is the area of ΔABC given m∠B = 95°, a = 22 feet, and c = 17 feet?use area = 1/2 ac sin B
area = 1/2 ac sin B
1/2 ( 22) ( 17) * (sin 95)
187 sin 95
186.2884085 ft^2
How do I calculate the shaded area of this shape ?
SOLUTION:
We are to calculate the shaded area of the given shape.
CONCEPT:
This is a triangle that a rectangle was cut out from.
To calculate the shaded area of the given shape, we are to find the area of the triangle and then subtract the area of the recangle that was cut out.
[tex]\begin{gathered} \text{Area of Triangle:} \\ A\text{ = }\frac{1}{2}\text{ base }\times\text{ height} \\ \\ A\text{ = }\frac{1}{2}\text{ }\times\text{ 6m }\times7m\text{ } \\ \\ A=21m^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of Rectangle:} \\ A=L\text{ }\times\text{ W } \\ A\text{ = 4m }\times\text{ 2m} \\ A=8m^2 \end{gathered}[/tex]The shaded area = Area of the triangle - Area of the rectangle
[tex]\begin{gathered} \text{Shaded area = 21 m}^2-8m^2 \\ \text{Shaded area = 13 m}^2 \end{gathered}[/tex]please help me with this. I have been trying to figure it out for a long time and I need to have dinner with my family very soon.
To subtract this polynomial, we would have to open the bracket
[tex]\begin{gathered} 9x^4+8x^3-6-(5x^2-8x+6) \\ 9x^4+8x^3-5x^2+8x-6-6=9x^4+8x^3-5x^2+8x-12^{} \end{gathered}[/tex]Remember, we only add and subtact directly , Algebraic characters of the same type only
and the same power only.
find the area of a square inscribed in a circle of a radius square root 70
The area of a square inscribed in a circle of a radius square root 70 is 140 units².
What is a square inscribed in a circle?A square is inscribed in a circle if its four vertices are on the circle's circumference. When a square is inscribed in a circle, the diameter of the circle must be equivalent to the diagonal of the square
Given:
The radius of the circle = √70 units
Let the side of the square inscribed in the circle be x units.
Diagonal of the square = [tex]\sqrt{x^{2} + x^{2} }[/tex] = [tex]\sqrt{2} x[/tex]
Diameter of the circle = 2 × √70 ≅ 16.7 units
Now,
Diagonal of the square = Diameter of the circle
[tex]\sqrt{2} x = 16.7[/tex]
[tex]x = \frac{16.7}{\sqrt{2} }[/tex]
x ≅ 11.83 units
So, the Area of the square = (side)² = x²
= (11.83)²
≅ 140 units²
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3y=-4x+5 y=-4/3x-8 are they parallel, perpendicular or neither
the lines are parallel.......
a rectangular flying carpet is 1 1/2 meters wide and 2 meters long what is the area of the carpet
The area of 1 1/2 meters wide and 2 meters long carpet is 3 meters².
As per the known fact, the area of rectangular object is calculated by performing multiplication of value of two sides. These two sides are length and width. Firstly converting width from mixed fraction to fraction -
Width = (2×1 + 1)/2
Width = 3/2 meters
Area = length × width
Keep the values in formula to find the value of area of rectangular flying carpet
Area = 3/2×2
Cancelling 2 as it is common in both numerator and denominator
Area = 3 meters²
Thus, the area of rectangular flying carpet is 3 meters².
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Question 2 George is 5 feet 8 inches tall. How many inches tall is he? (1foot = 12 inches) 58 inches O 60 inches O 68 inches O 12 inches
Answer:
68
Step-by-step explanation:
1 foot = 12 inches
Multiply 5 by 12 inches
5 feet = 60 inches
Add the extra 8 inches
60 + 8 = 68 inches
George is 68 inches tall.
Answer:
Step-by-step explanation:
George is 5 feet and 1 foot equals 12 inches, so do 12x5 + the actual 8 inches
12x5=60
60+8=68 inches total