Answer:
FV = PV x (1 + r)^n
where:
FV = future value
PV = present value (the amount to be deposited today)
r = interest rate per period (in this case, per year)
n = number of periods (in this case, 8 years)
Plugging in the given values, we get:
$60,000 = PV x (1 + 0.09)^8
Simplifying this equation:
PV = $60,000 / (1 + 0.09)^8
PV = $60,000 / 1.999^8
PV = $60,000 / 3.058
PV = $19,602.68
Therefore, the amount that needs to be deposited in the bank today to accumulate $60,000 in 8 years with an interest rate of 9% is $19,602.68.
I hope this helps.
Natasha is cutting construction paper into rectangles for a project. She needs to cut one rectangle that is 20 inches × 15 1 4 inches. She needs to cut another rectangle that is 10 1 2 inches by 10 1 4 inches. How many total square inches of construction paper does Natasha need for her project? Mixed number
what is the answer for this question
Answer:
The yellow region is 13.73 cm squared
Step-by-step explanation:
---
Area of square:
[tex]8 * 8 = 64 cm^2[/tex]
Area of the 4 quarter-circles:
[tex]4(\pi r^2)/4[/tex]
The fours cancel each other, we are left with:
[tex]\pi r^2[/tex]
r = 4, so substitute that, we get:
[tex]\pi 4^2 = 16 \pi cm^2[/tex]
Which can be approximated to 50.27 cm squared
Subtract the area of the circle from the square:
[tex]64 - 50.27 = 13.73 cm^2[/tex]
So the area of the yellow region is 13.73 cm squared
Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
United States Birth Rate (per 1000)
Birth Rate
A graph titled United States Birth Rate (per 1000) has year on the x-axis and birthrate on the y-axis. Points trend in a negative line.
Year
Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
a.
no correlation
b.
positive correlation; as time passes, the birth rate increases.
c.
positive correlation; as time passes, the birth rate decreases.
d.
negative correlation; as time passes, the birth rate decreases.
A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.
[tex]8 : 1/3\\[/tex]8 : 1/3
The ratio of 8 : 1/3 is equivalent to the simplified ratio of 24 : 1.
How to simplify the ratio?To analyze and describe the ratio 8 : 1/3, we need to convert the fraction to a ratio with a whole number. One way to do this is to express the fraction as a ratio with a denominator of 3:
1/3 = 1:3
Now we can rewrite the ratio 8 : 1/3 as:
8 : 1:3
We can simplify this ratio by multiplying both terms by 3 to get rid of the fractional term:
8 × 3 : 1:3 × 3
24 : 1
Therefore, the ratio 8 : 1/3 is equivalent to the simplified ratio 24 : 1. This means that for every unit in the second part of the ratio, there are 24 units in the first part of the ratio. In other words, the first part of the ratio is 24 times larger than the second part.
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Jeannie designs jewelry. The figure shows a
pendant on a necklace Jeannie is making. It is
composed of three individual beads.
The larger triangular bead cost $1.52. The
rectangular bead costs $0.42, and the smaller
triangular bead costs $0.92.
What is the cost per square millimeter of the
pendant? Round your answer to the nearest
hundredth.
Answer: ≅ $0.02
Step-by-step explanation:
First, lets find the area of the large triangle
0.5 x 14 x 11 = 77 mm^2
Next lets find the area of the middle rectangle:
4 x 14 = 56 mm^2
Last lets find the area of the small triange:
0.5 x 14 x 3 = 21 mm^2
So the total area is: 77 + 56 + 21 = 154 mm^2
the total cost is given to be: 1.52 + 0.42 + 0.92 = $2.86
dividing the cost by the area to find the cost/mm:
2.86/154 ≅ $0.02
Starting from rest, an object travels at a constant speed of 150 cm/s (centimeters per second) along a straight line. If d is the total distance in cm that the object has traveled at time t seconds, then which of the following gives the equation expressing d as a function of t, and the total distance d in meters that the object has traveled at time t = 2 seconds?
The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:
d = vt
where d is the distance, v is the constant speed, and t is the time elapsed.
In this case, the speed is 150 cm/s, so the equation is:
d = 150t
To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:
d = 150t
d = 150(2)
d = 300 cm
To convert to meters, we divide by 100:
d = 300/100
d = 3 meters
Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.
Smart Kitchen sells chocolate nonpareils in 8 oz. containers. Because the candy pieces are not uniform, the weight of each individual container varies slightly. A random sample of nine containers was weighed on a precision scale and the results are shown below:
8.09
8.20
8.03
7.86
7.87
8.06
8.43
7.99
8.08
Determine the interquartile range for this sample. Are there any outliers in this data set?
The interquartile range of the data will be 0.215.
How to calculate the valueThe lower half is:
7.86, 7.87, 7.99, 8.03
The median of the lower half is:
(Q1) = (7.87 + 7.99) / 2 = 7.93
The upper half is:
8.06, 8.08, 8.09, 8.20, 8.43
The median of the upper half is:
(Q3) = (8.09 + 8.20) / 2 = 8.145
The IQR is the difference between the third and first quartiles:
IQR = Q3 - Q1 = 8.145 - 7.93 = 0.215
Lower outlier threshold: Q1 - 1.5 x IQR = 7.93 - 1.5 x 0.215 = 7.5955
Upper outlier threshold: Q3 + 1.5 x IQR = 8.145 + 1.5 x 0.215 = 8.4795
None of the data points fall outside these thresholds, so there are no outliers in this data set.
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the line is parellel to graph of 2x-3y=7 and contains the point (-3,-3)
The equation of the line parallel to the graph of 2x - 3y = 7 and containing the point (-3,-3) is y = (2/3)x - 1.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph: 2x - 3y = 7.
First, we need to rearrange the given equation into slope-intercept form (y = mx + b) by solving for y:
2x - 3y = 7
-3y = -2x + 7
y = (2/3)x - 7/3
The slope of the given line is 2/3.
Hence, any line parallel to it will also have a slope of 2/3.
Using the point-slope form, we determine the equation of the line that passes through (-3,-3) and has a slope of 2/3:
y - y1 = m(x - x1)
y - (-3) = (2/3)(x - (-3))
y + 3 = (2/3)x + 2
y = (2/3)x - 1
Therefore, the equation of the line is y = (2/3)x - 1.
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at football practice, gustavo does push ups for 2 minutes for every 6 minutes playing if he plays for 42 minutes how many of push ups will he do
Answer:
14 mins
Step-by-step explanation:
2/6 = x/42
6x=84
x=14
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
[tex]f(0) = 6.2 \sqrt{4.5} + 18 = 31.2[/tex]
The perimeter of the quadrilateral is 34 centimeters. Find the length of each side.
x+8
x +4
2x - 2
x²-2x
Answer: x=4, sides = 12, 8, 6, 8
Step-by-step explain
Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.
X+8+x+4+2x-2+x²-2x=34
x²+2x+10=34
x²+2x-24
(x-4)(x+6)
x=4, x=-6
x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.
Now to find side lengths just plug in 4 for x
4+8=12
4+4=8
2*4-2=6
4*4-2*4=8
A school purchases boxes of paints for the annual painting competition. The expression below represents the total price for the order including delivery to the school. $11.75x + $20
Answer:
The expression $11.75x + $20 represents the total price for the order, including delivery to the school.
In this expression, 'x' represents the number of boxes of paints being purchased, and $11.75 represents the cost of each box. The term $11.75x represents the total cost of the boxes of paints based on the number of boxes being purchased.
The term $20 represents the delivery cost to the school, which is added to the total cost of the boxes of paints.
By multiplying the cost per box ($11.75) by the number of boxes (x) and adding the delivery cost ($20), you can calculate the total price for the order, including delivery.
PLEASE HELP! Showing all work, solve for x and why and round to nearest tenth
Answer:
x = 7.9 (nearest tenth)
y = 24.6° (nearest tenth)
Step-by-step explanation:
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:
[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 7.9.
[tex]\hrulefill[/tex]
The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 24.6°.
For the right triangle below, find the measure of the angle.
Figure is not to scale.
For the given right-angled triangle the measure of the angle is 11.30°.
Given adjacent base of the triangle = 10
given opposite side of the triangle = 2
To find out the angle we can use a little bit of trigonometry. By trigonometry, we know that tan ∠ = opposite side / adjacent side.
So, we can use the above tan ∠ relation to find the angle.
Tan ∠ = opposite side / adjacent side
Tan ∠ = 2/10
Tan ∠ = 1/5
∠ = Tan⁻¹(1/5)
∠ = 11.30°.
From the above explanation, we can conclude that the measure of the angle for the given right triangle is 11.30°.
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Navid earns a basic wage of $10.25 an hour. He works for 40 hours a week. He earns 20% more than his basic wage when he works overtime. Navid wants to earn at least $500 this week. Calculate the total number of hours he needs to work. Give your answer to the nearest hour.
a. Use the graph to approximate the value of the car after 4 years.
b. Use the graph to approximate the value of the car after 5 years.
c. Use the graph to approximate when the car will be worth half its original value. (Determine the number of years.)
The car will be worth half its original value after 4 years
How to solveA graph for straight-line depreciation for a car is given.
a
The number of years the car totally depreciates is 8 years as seen in the graph which is x -intercept.
Step 3/7
The model makes straight-line depreciation. In a straight line depreciation equation, the intercepts are
(0, maximum car value) and (maximum lifespan,0)
Let y represent the value of the car at any time during its lifetime. The minimum y -value is zero dollars and the maximum y -value is the purchase price of $25,600
The intercepts are (0, 25, 600) and (8,0)
Determine the slope of the equation.
Two points determine a line, so only two points are needed to determine the slope of a line.
Let the coordinates of the -intercept be the first point. That is, (xi,yi) = (0, 25, 600)
Let the coordinates of the -intercept be the second point. That is (x2, y2)= (8,0)
Use the slope ratio as shown below;
The slope of the depreciation equation is.
-3200
The general form for the equation of a straight line is:
y = mx + b
Where m represents the slope of the line and b represents the y-intercept.
The slope is -3,200 and the -intercept is 25,600 as obtained.
Therefore, the straight line depreciation equation is:
y = -3,200x + 25,600
Therefore, the value of the car after 4 years is $12,800
b.
Use the depreciation equation and substitute x=5 years to find the car worth after 5 years.
Therefore, the value of the car after 5 years is $9,600
c.
The half value of the car is half of $25,600 which is $12,800
The car will be worth half its original value after 4 years
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During a sale, a store offered a 25% discount on a bed that originally sold for $800. After the sale, the discounted price of the bed was marked up by 25%. What was the price of the bed after the markup? Round to the nearest cent.
The price of the bed after mark up is $475.00
What is discount?Discount results in the reduction of the selling price of the product, which makes it more attractive for the customer.
The first discount given is 25% , therefore the price of the bed before mark up is
25/100 × 800
= 25×8
= 200
the price before mark up = 800-200 = $600
Another 25% is given after the first sale, there the price of the bed after mark up is
25/100 × 600
=$ 125
price after markup = 600-125
= $475.00
therefore the price of the bed after markup is $475.00
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PLS HELP IM FAILING ALGEBRA
Help me out please y’all
The piecewise function is
f(x) = { x -3 , x≤3
8, -3 < x ≤ 5
x+10, x>6
For values less than or equal to -3, we have a line with a positive slope. We have two lines, y = x - 2, and y = x - 3.
1. For y = x - 2
-5 = -3 - 2= -5
2. For y = x - 3
-5 = -3-3 = -6
The fact that the domain is specified for x less than -3 further demonstrates that the first choice is not an option.
Additionally, we know that the function's value is equal to 8 for the range from x greater than -3 to less than or equal to 5.
Additionally, the equation is given as y = -x + 10 and the line has a negative slope for values greater than 6.
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I need help with the answer to the photo provieded
Answer:
26
Step-by-step explanation:
Line g has an equation of y = 2x + 1. Line h includes the point (-5, 2) and is perpendicular
to line g. What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Submit
In 2010, the sea turtle population was twice the amount of turtles as in 2005. How many sea turtles were there in 2010?
Without knowing the exact number of turtles in 2005, we cannot determine the exact number of turtles in 2010. However, we can use the information given to set up an equation.
Let x be the number of sea turtles in 2005.
According to the problem, the number of sea turtles in 2010 was twice the amount in 2005, or 2x.
We can set up an equation:
2x = number of sea turtles in 2010
We don't know the exact value of x, so we cannot solve for the number of turtles in 2010.
Need help with this question. Been stuck on this for 20 mins.
Answer:
see below
Step-by-step explanation:
The Reason for #1 is literally GIVEN to you.
Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.
Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.
Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.
Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.
1. A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut up into children's bricks. Each brick is a cube of side 3 cm.
(a) Find the largest number of bricks that can be cut from the block.
(b) Find the volume of wood that is left.
The dimensions of the rectangular block indicates;
(a) The largest number of bricks that can be cut from the block is 48 bricks
(b) The volume of the wood left is 216 cm³
What is the volume of a rectangular block?The volume of the rectangular block is the product of the length, L, width, W, and height, H.
1. The dimensions of the rectangular block indicates that the block volume is; V = 24 cm × 9 cm × 7 cm = 1,512 cm³
The largest number of bricks that have side lengths of 3 cm that can be cut from the block is therefore;
Number of cubes; (24)/3 × (9)/3 × (7)/3 ⇒ 8 × 3 × 2 = 48
48 cube bricks can be cut from the block(b) The volume of wood left = 1512 - 48 × 3 × 3 × 3 = 216
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Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer: 100.48 cubic feet
Step-by-step explanation:
Factor the expression. x^2-14x-32
Answer:
[tex](x-2)(x+16)[/tex]
Step-by-step explanation:
Use graphing calculator and find the x-intercepts.
NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The trigonometry functions when evaluated are shown below
Evaluating the trigonometry functionsIn trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.
They are defined as follows:
sin A = opposite side/hypotenuse.
cos A = adjacent side/hypotenuse.
tan A = opposite side/adjacent side.
So, we have
Figure 1
sin A = 6/9cos A = √5/3tan A = 6/√5Figure 2
sin A = √2/2cos A = √2/2tan A = 1Figure 3
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Santiago is going to see a movie and is taking his 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $4.50 each. How much total money would Santiago have to pay for his family if he were to buy 6 snacks for everybody to share? How much would Santiago have to pay if he bought x snacks for everybody to share?
Answer:
25$ if the tickets were involved it would be 70$
Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.
Explanation:The topic of this question is
Mathematics
, specifically about using multiplication and addition in problem-solving.
Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.
Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.
Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.
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Michael purchased stereo equipment for $2500. His wife claims that was not a smart investment because stereo equipment decreases in value at a rate of 9% per year. How much will his stereo equipment be be worth after 8 years?
Based on an exponential decay factor, Michael's stereo equipment will be worth $2,116 after 8 years, given the decreasing rate of 9% per year.
What is an exponential decay factor?The decay factor is represented by (1 - r), where r is the constant periodic decreasing rate.
The decay factor is used in exponential decay functions to determine the depreciated value of an asset.
Current price of stereo equipment = $2,500
Annual decreasing rate = 9%
Decrease factor = 0.91 (100% - 9%)
The number of years = 8 years
Value of the equipment after 8 years = ($2,500 x 0.91^8)
= $2,116.125 ($2,500 x 0.47025)
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 Cooper can purchase a item for $45.00, Which store has the best buy?
A. Store 1: 25% off coupon
B. Store 2: $15 dollars off
C. Store 3: 10% off
I’ll give brainly please help me