Answer:
Ruth was out of Portland at 35mph at 7:00 am
so at 9 am, she was 70 miles ahead of Michael
but Michael was 20 miles ahead by 3 pm.
so in 6 hours, he went past Ruth by 90 miles which is 90/6 = 15mph
Michael speed = ruth speed + 15. = 35 + 15 = 50mph
To the nearest tenth, what is the area of the shaded segment when AG = 6 ft?
10.3 ft2
21.1 ft2
1.7 ft2
28.3 ft2
Answer:
Option A is correct.
Step-by-step explanation:
Given:
AG = 6 ft ⇒ Radius of the circle , r = 6 ft
⇒ GB = AG = 6 ft
To find: Area of shaded Segment.
Area of Shaded Segment = Area of Sector AGBA - Area of Δ AGB
Sector AGBA forming 90° angle at center. [tex]\implies\,\theta=90^{\circ}[/tex]
Area of Sector = [tex]\frac{\theta}{360}\times\pi r^2[/tex]
Area of Sector AGBA = [tex]\frac{90}{360}\times3.14\times6^2[/tex]
= [tex]\frac{1}{4}\times3.14\times36[/tex]
= [tex]28.26\:ft^2[/tex]
ΔAGB is a right angled triangle.
So, Area of ΔAGB = [tex]\frac{1}{2}\times AG\times GB[/tex]
= [tex]\frac{1}{2}\times6\times6[/tex]
= [tex]6\times3[/tex]
= [tex]18\:ft^2[/tex]
Area of Shaded Segment = 28.26 - 18 = 10.26 ≈ 10.3 ft²
Therefore, Option A is correct.
A box has a volume of 135 feet3. The length is same as the height, and the width is 5 times the length. What are the dimensions of the box?
The dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.
Explanation:This is a classic problem of volume where we need to consider the volume formula of a box, which is length × width × height. The question states that the box has a volume of 135 cubic feet, with the length being the same as the height, and the width being 5 times the length.
To find the dimensions of the box, we can set up the equation: length × 5 ×length × length = 135. Simplifying, we get that the length is the cube root of 135/5, which equals to 3. Thus, the dimensions of the box are: length=3 feet, width=15 feet, and height=3 feet.
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I'm a little confused on how to solve this, can anybody help?
Solve the following system of equations and show all work.
y = x^2 + 3
y = x + 5
10,14 and 18 can someone answer Pls pls
Answer:
10) 35
14) x = 1/2
18) 10 cm
Explanation:
For question 10, we can set up a proportional equation, cross-multiply and solve for the missing number:
[tex]\frac{x}{14} = \frac{5}{2}[/tex]
2x = 14(5)
2x = 70
2x / 2 = 70 / 2
x = 35
The missing number is 35
For question 14, we isolate variables on one side of the equation and constants on the other by performing whatever operations are necessary and then solve for the variable:
14x + 2 = 9
14x + 2 - 2 = 9 - 2
14x + 0 = 7
14x = 7
14x / 14 = 7 / 14
x = 7 / 14
x = 1/2
x = [tex]\frac{1}{2}[/tex]
For question 18, there are 10 millimeters (mm) in 1 centimeter (cm) so we can use this relationship so set up a conversion factor and cross-multiply to find the missing value like we did in question 10:
[tex]\frac{10}{1} = \frac{100}{x}[/tex]
10x = 100(1)
10x = 100
10x / 10 = 100 / 10
x = 10
There are 10 cm in 100 mm.
The sum of three consecutive integers is 162. what is the smallest og these integers?
A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area (A=lw), how long is the rectangle? a. 21 inches b. 340 inches c. 20 inches d. 15 inches
Answer:
a - 21 inches
Step-by-step explanation:
Following the formula [tex]Area = l*w[/tex], we can find the length of the rectangle by plugging in values into the formula, then solving for [tex]l[/tex].
[tex]357=l*17[/tex]
[tex]\frac{357}{17} =\frac{l*17}{17} \\\\21=l\\l=21[/tex]
A bird seed feeder has the approximate shape of a cone with a diameter of 12 centimeters and a height of 25.5 centimeters. What is the best approximation for the volume of the bird seed feeder? 320.44 cm³ 961.33 cm³ 2883.98 cm³ 3845.31 cm³
Answer: Volume of the bird seed feeder = 961.33 cm³
Step-by-step explanation:
Given shape of bird seed feeder of a cone
Diameter =12cm
So Radius =D/2 =12/2
=6cm
Height = 25.5cm
Volume of cone = [tex]\frac{1}{3 }\times \pi r^{2}h[/tex]
Volume = [tex]\frac{1}{3}\times\pi6^{2}\times25.5[/tex]
Volume =[tex]\frac{1}{3}\times \frac{22}{7}\times36\times25.5[/tex]
Volume = [tex]\frac{20196}{21}[/tex]
Volume = 961.33 cm³(approx)
So the volume of bird seed feeder is 961.33 cm³
Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20. If she plans for them in 12 equal payments, what’s her monthly cost?
The monthly cost will be $62.88 if Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20.
What is debt?It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
We know the formula for the monthly payment:
[tex]\rm Monthly \ Payment \:=\:\dfrac{\left A\left(i\right)\left(1+i\right)^{n}\right}{\left(1+i\right)^{n}-1}[/tex]
It is given that:
Cathy is purchasing a DVD player and tv at the local electronic store.
The DVD player costs $49.36 and the tv cost $705.20.
If she plans for them in 12 equal payments,
Total cost(combining the cost of the DVD player and TV cost):
= $49.36 + $705.20
= $754.56
Per month payment = $754.56/12
Per month payment = $62.88
Thus, the monthly cost will be $62.88 if Cathy is purchasing a DVD player and tv at the local electronic store. The DVD player costs $49.36 and the tv cost $705.20.
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Which situation involves descriptive statistics?
A. The survey shows that 1 in 3 moviegoers would attend a midnight showing.
B. A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.
C. A reporter surveys some commuters in a city to estimate what percent of city’s commuters spend 45 minutes or more getting to work.
D. Eighty percent of the recipes in a cookbook require salt.
All options involve descriptive statistics, but option B is a classic example as it involves computation of a median, an important tool in descriptive statistics.
Explanation:Descriptive statistics is used to describe, show or summarize data in a meaningful way. All the options given indicate the use of descriptive statistics because they all describe a given population or set of data using numerical measures. However, the most classical use of descriptive statistics is found in option B: 'A recent survey of the cost of new homes in the United States shows that the median price of a new home is up $15,000 since last year.' This situation involves the computation of a median, a common measure in descriptive statistics, to summarize property price data.
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How much more would $1,000 earn in 5 years in an account compounded continuously than an account compounded quarterly if the interest rate on both accounts is $3.7%
Answer: There is a difference of $ 1.0228.
Explanation: Given, initial amount or principal = $ 1000,
Time= 5 years and given compound rate of interest = $3.7%
Now, Since the amount in compound continuously,
[tex]A= Pe^{rt}[/tex] , where, r is the rate of compound interest, P is the principal amount and t is the time.
Here, P=$ 1000, t=5 years and r= $3.7%,
Thus, amount in compound continuously , [tex]A=1000e^{3.7\times5/100}[/tex]
⇒[tex]A=1000e^{18.5}=1000\times 1.20321844013=1203.21844013[/tex]
Therefore, interest in this compound continuously rate =1203.21844013-1000=203.21844013
now, Since the amount in compound quarterly,
[tex]A=P(1+\frac{r/4}{100} )^{4t}[/tex], where, r is the rate of compound interest, P is the principal amount and t is the time.
Thus, amount in compound quarterly, [tex]A=1000(1+\frac{3.7/4}{100} )^{4\times5}[/tex]
⇒[tex]A=1000(1+\frac{3.7}{400} )^{20}[/tex]
⇒[tex]A=1000(1+\frac{3.7}{400} )^{20}[/tex]
⇒[tex]A= 1202.19567617[/tex]
Therefore, interest in this compound quarterly rate=1202.19567617-1000=202.19567617
So, the difference in these interests=203.21844013-202.19567617=1.02276396 ≈1.0228
Becky is 18 and would like to buy a house when she is 36. What is the discount factor for today's prices if the housing values increase 6% per year?
Answer: 35.0%
Step-by-step explanation:
Can someone help with number 3
A recipe for cookies calls for 2⁄3 of a cup of chocolate chips and 4 cups of flour. If you want to make a bigger batch, using 6 cups of flour, how many cups of chocolate chips will you need?
Find the point on the line 4x+4y+5=0 which is closest to the point (−2,−3).
The function is defined below. find all values of that are not in the domain of . if there is more than one value, separate them with commas.
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5
1/8hours in the afternoon, how many hours does she work in the evening?
Answer:
She worked [tex]6\frac{7}{8}[/tex] hours in evening.
Step-by-step explanation:
Suppose, x be the hours waitress worked in evening,
Given,
She works 1.75 hours less in the afternoon than in the evening.
Thus, the number of hours she worked in afternoon = x - 1.75,
According to the question,
[tex]x-1.75 = 5\frac{1}{8}[/tex]
[tex]x-\frac{175}{100}=\frac{41}{8}[/tex]
[tex]x-\frac{7}{4}=\frac{41}{8}[/tex]
[tex]x=\frac{41}{8}+\frac{7}{4}[/tex]
[tex]x=\frac{41+14}{8}[/tex]
[tex]x=\frac{55}{8}=6\frac{7}{8}[/tex]
Therefore, she worked [tex]6\frac{7}{8}[/tex] hours in evening.
if a tree diagram were drawn to determine the number of possible outcomes when choosing one of 5 salads, one of 6 entrees, and one of 9 desserts, how many leaves would there be?
Answer:
270
Step-by-step explanation:
Just multiply.
5*6*9=270
Answer: There would be 270 leaves of a tree diagram.
Step-by-step explanation:
Since we have given that
Number of salads = 5
Number of entrees = 6
Number of desserts = 9
If we draw a tree diagram, we need to find the number of leaves there would be :
So, the number of leaves there would be is given by
[tex]5\times 6\times 9\\\\=270[/tex]
Hence, there would be 270 leaves of a tree diagram.
The coefficient of the term 76x2 is:
(2 is the exponent of 76x)
The amount of money in Nadia’s savings account is represented by the recursive formula mc010-1.jpg. If mc010-2.jpg, what are the first two numbers in the sequence? $25.36, $75.99 $50.00, $101.25 $101.25, $153.78 $75.99, $127.89
Answer:
a is correct
Step-by-step explanation:
help needed please.
What is the length of chord JK?
An ice cream cone has a diameter of 2 inches and a height of 5 inches. What is the volume of the ice cream cone? Round your answer to the nearest hundredth. (Use 3.14 for π.) 10.47 in.3 20.93 in.3 5.23 in.3 15.7 in.3
Answer:
The answer 5.23
Step-by-step explanation:
The perimeter of a rectangular field is 242 yards if the width of the field is 54 yards what is the lenght
Which expression is equivalent to (2x^5+7x^3)-(5x^2-4x^3)
Answer:
2x^5+11x^3−5x^2
Step-by-step explanation:
Math Papa
In FGH, mF = 65, mG = 55, and mH = 60. Which side of FGH is the shortest?
Answer: Fh is the shortest
(09.01 LC) Look at the figure below: A circle is shown with the center O. OP is a segment joining center O to a point P on the circle. MN is a line touching the cir Which is the tangent to the circle? (6 points) Segment OP Line ST Line MN Segment QR
Answer:
Line MN is the answer
Step-by-step explanation:
The number of nails of a given length is normally distributed with a mean length of 5.00 in. and a standard deviation of 0.03 in. Find the number of nails in a bag of 120 that are less than 4.94 in. long.
About 3 nails is correct on grad point
What is the solution to the equation 7(a – 10) = 13 – 2(2a + 3)
Answer:
[tex]a=7[/tex]
Step-by-step explanation:
we have
[tex]7(a-10)=13-2(2a+3)[/tex]
Solve for a
[tex]7a-70=13-4a-6[/tex]
Group terms that contain the same variable and move the constants to the other side
[tex]7a+4a=13-6+70[/tex]
Combine like terms
[tex]11a=77[/tex]
Divide by [tex]11[/tex] both sides
[tex]a=7[/tex]
How do you factor the expression #2x^2+ 5x + 3#?
If the sample size gets smaller, how does that affect the shape of the smapling distribution of sample means