Answer:
approximately 462.24
Step-by-step explanation:
Gertrude made eight more than three times the number of apple pies that Ruth made. If Gertrude made 14 pies, how many did Ruth make?( hint: let p equal the number of pies Ruth made.)
Wich is the least common multiple of 12 and 8?
Answer: 24
Step-by-step explanation: The first few multiples of 8 are: 8, 16, 24, 32, 40, and 48. The first multiples of 12 are: 12, 24, 36, 48, 60, and 72.
...
Step 1: List the Multiples of Each Number.
Oceanside Bike Rental Shop charges 17 dollars plus 7 dollars an hour for renting a bike. Mike paid 66 dollars to rent a bike. How many hours did he pay to have the bike checked out ?
Answer:
7 hours
Step-by-step explanation:
The hourly charge was $66 -17 = $49. That charge was $7/hour so Mike had the bike for ...
$49/($7/hour) = 7 hours.
__
You could write an equation for the total charge, then set it equal to 66 and find the solution that way. For h hours, the charge is ...
charge = 17 + 7h
66 = 17 +7h
49 = 7h . . . . . . . . maybe this looks familiar
49/7 = h = 7 . . . . divide by the coefficient of h
Mike had the bike for 7 hours.
A television program is 2 hours and 40 minutes long.
a)It starts at 22:45
at which time does it finish?
b)the program contains 8 ADs breaks,each of which lasts 3 min.
find the fraction of the 2 hours 40 min that is taken by ADs.
Give your answer in its simplest form.
Final answer:
The television program finishes at 00:25 after starting at 22:45 and running for 2 hours and 40 minutes. The fraction of the program's total time taken by 8 ad breaks, each lasting 3 minutes, is 3/20 of the total program time.
Explanation:
To calculate the finish time of the television program that starts at 22:45 and is 2 hours and 40 minutes long, we add the duration of the program to the start time. Firstly, we convert 2 hours and 40 minutes into minutes only to simplify addition. That is 160 minutes (120 minutes for 2 hours and 40 minutes for the remaining time). When we add 160 minutes to 22:45, we need to be careful due to the change of day at midnight.
Adding the minutes part first, 45 minutes + 40 minutes = 85 minutes. We subtract 60 minutes to account for one full hour giving us 25 minutes and add an hour to the hour part. 22:45 therefore becomes 23:25 with an additional 1 hour to be added.
We are left with 1 hour to add to 23:25, which simply gets us to 00:25, or 25 minutes past midnight. The television program finishes at 00:25.
Calculating the Fraction of Time Taken by Ads
The program contains 8 ad breaks, each of which lasts 3 minutes. The total time taken by the ads is 8 breaks × 3 minutes per break = 24 minutes of ads.
To find the fraction of time taken by the ads, we need the total duration in minutes, which is 2 hours and 40 minutes or 160 minutes. The fraction is therefore 24/160, which simplifies to 3/20 when we divide both the numerator and the denominator by 8.
Thus, the fraction of the 2 hours and 40 minutes that is taken by ads is 3/20.
A large manufacturer that sells consumer products on-line wishes to publicize its customer satisfaction in an advertisement. Specifically, it wants to state that over 90% of the manufacturer's customers would tell a friend to buy a product from the manufacturer. The manufacturer selects a random sample of 400 customers from its database, contacts them via email and asks them the question "Would you tell a friend to buy a product from us?" 372 say Yes, and 28 say No. Is thos enough evidence for this manufacturer to state that more than 90% of its costumers would tell their friend to buy a product from the manufacturer?
Answer:
[tex]z=\frac{0.93 -0.9}{\sqrt{\frac{0.9(1-0.9)}{400}}}=2[/tex]
[tex]p_v =P(z>2)=0.0228[/tex]
So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who say yes is significantly higher than 0.9 or 90%.
Step-by-step explanation:
Data given and notation
n=400 represent the random sample taken
X=372 represent the number of people who say yes
[tex]\hat p=\frac{372}{400}=0.93[/tex] estimated proportion of people who say yes
[tex]p_o=0.9[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that that more than 90% of its costumers would tell their friend to buy a product from the manufacturer.:
Null hypothesis:[tex]p\leq 0.9[/tex]
Alternative hypothesis:[tex]p > 0.9[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.93 -0.9}{\sqrt{\frac{0.9(1-0.9)}{400}}}=2[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level assumed for this case is [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
[tex]p_v =P(z>2)=0.0228[/tex]
So the p value obtained was a very low value and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who say yes is significantly higher than 0.9 or 90%.
A garden is in the shape of a rectangle 85 m by 50m.
Flowers are grown in 32% of the garden.
The rest of the garden is grass.
Work out the area of the garden that is grass.
Show your working out.
Answer:
2,890 meters^2 is grass
Step-by-step explanation:
First find the area of the garden
Area of a rectangle can be found using:
a=lw
a=85*50
a=4,250 meters^2
We know that 32% of the area is flowers, so we can multiply 32% and 4250
32%*4250
Convert 32% to a decimal by dividing by 100
32%/100=0.32
0.32*4250=1360
So, 1360 meters^2 is flowers.
The rest must be grass, so we can find the difference between the total area and the flowers
4250-1360=2890
So, 2,890 meters^2 is grass
Answer:
The answer to your question is 2890 m²
Step-by-step explanation:
Data
length = 85 m
width = 50 m
32% are flowers
Process
1.- Calculate the area of the garden
Area = length x width
-Substitution
Area = 85 x 50
= 4250 m²
2.- Calculate the area of the garden that are flowers
4250 ----------------- 100%
x ------------------ 32%
x = (32 x 4250) / 100
x = 136000/100
x = 1360 m² are flowers
3.- Calculate the area of the garden that is grass
Area of grass = 4250 - 1360
Area of grass = 2890 m²
please assist me with this problem
Answer:
a) [tex]\sqrt{64+x^2}[/tex]
b) 15
Step-by-step explanation:
a) We know that AB = 8 and BC = x. We can use the Pythagorean Theorem, which states that for a right triangle with sides a, b, and c: [tex]a^2 +b^2=c^2[/tex] , where a and b are the shortest sides and c is the longest.
Here, AB = a = 8 and BC = b = x. So, AC = c. Then:
[tex]AB^2+BC^2=AC^2[/tex]
[tex]8^2+x^2=AC^2[/tex]
[tex]AC=\sqrt{64+x^2}[/tex]
b) We know that AC - AB = 9. Since AB = 8, then AC = 9 + 8 = 17. We also have the expression from above, so set them equal:
[tex]AC=\sqrt{64+x^2}=17[/tex]
[tex]64+x^2=289[/tex]
[tex]x^2=225[/tex]
x = 15
Hope this helps!
Answer:
sqrt(x^2 +64) = AC
x = 15
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2 + b^2 =c^2 a and b are the legs and c is the hypotenuse
We know the legs are x and 8
x^2 + 8^2 = AC^2
x^2 + 64= AC^2
Solving for AC
Take the square root of each side
sqrt(x^2 + 64) = sqrt(AC^2)
sqrt(x^2 +64) = AC
We are given AC - AB = 9
We know AB = 8
AC -8 =9
Add 8 to each side
AC -8+8 = 9+8
AC = 17
AC is the hypotenuse,
x^2 + 64= AC^2
x^2 +64 = 17^2
x^2 +64 = 289
Subtract 64 from each side
x^2 +64-64 = 289-64
x^2 =225
Take the square root
sqrt(x^2) = sqrt(225)
x =15
The circus returned home and the animal trainers friend asked how many lions were on the train. The trainer answer "7 times as many lions than other animals (not lions). Then the friend asked about the bears." there were a seventh as many bears as other animals", replied the trainer. Then the friend asked about the elephants. How should the trainer respond to the question?
Answer:
Step-by-step explanation:
Solution:-
- We will denote:
Number of Lions = x
Number of bears = y
Number of elephants = z
Any other animal = T
- Now we will mathematically each statement given by the trainer.
Statement 1:
"7 times as many lions than other animals (not lions)."
- There were 7 times as many lions than any other animals i.e ( bears and elephants). So we can express:
x = 7*( x + y + T) .... E 1
Statement 2:
"there were a seventh as many bears as other animals"
- There were 1/7 as many bears than any other animals i.e ( lions and elephants). So we can express:
y = (x+z+T) / 7 ... E2
- Now combine two decrypted mathematical expressions.
x + y + z = T
7T + T/7 + z = T
A school bus company charges$ 2.70 pee kilometre to ferry 36 children for an outing.How much does each child have to pay if the distance trevelled for the trip is 32.5 kimometre
Answer:
each child must pay $ 87.75
Step-by-step explanation:
$87.75
Step-by-step explanation:
32 kilos part:
2.70 x 32 = 86.4
0.5 part: half of 2.70 is 1.35, so just add it to 86.4
in a geometric sequence, the fourth term is 8 times the first term. the sum of the first 10 terms is 2557.5. find the 10th term of this sequence.
Answer: 1280
Step-by-step explanation:
The fourth term is 8 times the first term.
The fourth term = [tex]ar^3[/tex]
[tex]ar^{3} = 8a[/tex]
To find the common ratio:
∴ [tex]\frac{ar^3}{a} = \frac{8a}{a}\\[/tex]
∴ [tex]r^3 = 8\\r = 2\\[/tex]
Common ratio = 2
To find the nth number of terms = [tex]\frac{a(r^n -1)}{r-1\\}[/tex]
∴ [tex]\frac{a(2^{10} -1)}{2-1}[/tex]
∴ [tex]1023a\\[/tex]
The sum of 10 terms = 1023a
The sum of 10 terms = 2557.5
∵ 2557.5 = 1023a
∵ [tex]a = \frac{5}{2}[/tex]
To find the 10th term:
∴ [tex]ar^9\\[/tex]
∴ [tex]\frac{5}{2} *2^9[/tex]
⇒ 1280 ║ answer.
From the question given above, we were told that the fourth term is 8 times the first term. This can be written as:
T₄ = 8a
But
T₄ = ar³
a => is the first term
r => is the common ratio
Thus,
ar³ = 8a
Solving for the common ratio (r):
ar³ = 8a
Divide both side by a
r³ = 8
Take the cube root of both side
r = ³√8
r = 2
Thus, the common ratio (r) is 2
Next, we shall determine the first term (a). This can be obtained as follow:
Sum of 10th term (S₁₀) = 2557.5
Common ratio (r) = 2
Number of term (n) = 10
First term (a) =?Sₙ = a[rⁿ – 1] / r – 1
2557.5 = a[2¹⁰ – 1] / 2 – 1
2557.5 = a[1024 – 1]
2557.5 = 1023a
Divide both side by 1023
a = 2557.5 / 1023
a = 2.5
Thus, the first term is 2.5
Finally, we shall determine the 10th term of the sequence. This can be obtained as follow:
Common ratio (r) = 2
First term (a) = 2.5
10th term (T₁₀) =?T₁₀ = ar⁹
T₁₀ = 2.5 × 2⁹
T₁₀ = 2.5 × 512
T₁₀ = 1280
Therefore, the 10th term of the sequence is 1280
Learn more: https://brainly.com/question/16929076
Cement was poured to make two rectangular prism the prism were stacked as shown 4 feet 3 feet 4 feet 3 feet 2 feet what are lengths , width, height in feet of the smaller rectangular prism
Final answer:
Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.
Explanation:
Given:
Lengths of the larger prism: 4 feet, 3 feet, 4 feet
Dimensions of the stacked prisms: 4 feet, 3 feet, 2 feet
Let: The lengths, widths, and heights of the smaller prism be L, W, and H respectively.
Two proportions:
4/L = 4/3
3/W = 3/2
Solving the proportions, we find that the lengths, width, and height of the smaller prism are 3 feet, 2 feet, and 3 feet respectively.
WILL GIVE 1ST RIGHT ANSWER BRAINIEST!
After two numbers are removed from the list 9,13,15,17,19,23,31,49, the average and the median each increase by 2. What is the product of the two numbers that were removed?
Answer:
247
Step-by-step explanation:
Hello!
We can begin by finding the average and median before two numbers are removed.
(9 + 13 + 15 + 17 + 19 + 23 + 31 + 49) / 8 = 22
And the median!
(17 + 19)/ 2 = 18
Since we know that the average and median will increase by 2, we will have the median after removal as 20, and the average, 24.
For the average, we can see that the total must be 144, that's what 24 * 6 is.
19 must have been one of the numbers because (17 + 23) / 2 = 20.
That's 32 less than the original sum of 176.
So if one of the removed numbers is 19, the other must be 13.
13 * 19 = 247
Thus, the product of the removed numbers are [tex]\boxed{247}[/tex].
Hope this helps!
Please help!
Two semicircles are placed in a rectangle. The width of the rectangle is 7 cm.
Find the area of the shaded region. Use the value 3.14 for pi , and do not round your answer.
Answer:
Total length of the rectangle = 14+14= 28cm
width= 7 cm
Area of the rectangle = 28×7cm²
= 196 cm²
Area of 2 semicircles = Area of 1 circle
= π(7)² = 3.14×49= 153.86cm²
Area of the shaded region = 196-153.86
= 42.14 cm²
Answer: 42.14 [tex]cm^2[/tex]
Step-by-step explanation:
Assuming that the width of the rectangle is 7 cm, the semi-circle's radius is also 7 cm.
Let's calculate the area of the two semi-circles, which in total makes a whole circle.
The formula for a circle is [tex]a=2\pi r^2[/tex]
Since r = 7, plug it in the formula:
[tex]a=2\pi (7)^2[/tex]
[tex]a=49\pi =153.86 cm^2[/tex]
Now, to figure out the length of the rectangle, look at the semi-circles. Their radius is 7 cm, so their diameter is 14 cm. We have two semi-circles with the diameter (14 cm), so we can say that the width is 28 cm.
Area of a rectangle: [tex]a=lw[/tex]
[tex]a=7*28=196cm^2[/tex]
To find the area of the shaded region, we subtract the area of the semi-circles to the rectangle, which should be:
[tex]196 - 153.86=42.14 cm^2[/tex]
How would you write twelve more than the quotient of a number and five
Answer:
n/5 +12
Step-by-step explanation:
Simplify: 27 : 54 : 9
Answer:
3 : 6 : 1
Step-by-step explanation:
The common multiple between these numbers is 9, so divide everything by nine.
Answer:
3:6:1
Step-by-step explanation:
27/9=3
54/9=6
9/9=1
3:6:1
I hope this helps!
The box plots show the average wind speeds, in miles per hour, for various cities in two different countries
Average Wind Speeds of Cities in Country A
D
's
8
9
10 11
Average Wind Speeds of Cities in Country B
Which statement describes the symmetry of the data in the two box plots?
The data in country A are more symmetric than the data in country B.
The data in country B are more symmetric than the data in country A
The data in both countries have about the same symmetry.
The symmetry of the data cannot be determined by looking at the box plots.
What is the answer
Answer:
the answer is b.
Step-by-step explanation:
Which sentence signals a major shift in the action of the story?
A "The suns beat down on her neck as she stepped closer to examine the chart
B "She stamped her foot and gave a loud groan."
C Kari suddenly remembered a magic trick she had performed at her little brother's
birthday party.
D
"Then she watched as the pile of snow came falling down to test on the dirt that had
been underneath the grass field."
Answer:
i think, it is option c.
Each lap Jeffery runs is 1 tenth of a mile. He wants to run 3 fifths
of a mile
How many laps does Jeffery need to run?
Answer:
6 laps
Step-by-step explanation:
Jeffery needs to run 3 laps.
Explanation:To find the number of laps that Jeffery needs to run, we can set up a proportion. We know that 1 lap is equal to 1 tenth of a mile, so we can set up the following proportion:
1 lap / 1 tenth mile = x laps / 3 fifths mile
Cross-multiplying and solving for x, we get:
x = (1 lap * 3 fifths mile) / (1 tenth mile)
x = 3 laps / 1 lap
x = 3
Therefore, Jeffery needs to run 3 laps.
Learn more about Proportion here:https://brainly.com/question/34018947
#SPJ2
Which expressions are equivalent to the one below? Check all that apply.
3^4 • 3^X
Answer:
C and D
Step-by-step explanation:
Answer:
its c and d
Step-by-step explanation:
Which of the following best describes the equation below?
y = 5x - 7
A.
neither linear nor nonlinear
B.
nonlinear
C.
linear
D.
both linear and nonlinear
Answer:
Step-by-step explanation:
B.
nonlinear
Answer:
Step-by-step explanation:
Work out the answers to:
a) 6 × (-3)
b) (-5) × 4
c) (-9) × (-2)
Step-by-step explanation:
a. 6 * (-3) = - 18
b. (-5) * 4 = - 20
c. (-9) * (-2) = 18
What is the value of x in 15x-15=30
Answer: 3
15(3)-15=30
45-15=30
30=30
15x-15=30
15x=45
x=3
Answer:
x=3Step-by-step explanation:
[tex]\sf 15x-15=30[/tex]
[tex]\sf 15x-15+15=30+15[/tex]
[tex]\sf 15x=45[/tex]
[tex]\sf \frac{15x}{15}=\frac{45}{15}[/tex]
[tex]\sf x=3[/tex]
What is 4/24 x 2/3 =
Simplied
Answer:
all work is shown and pictured
please helpppp (::: this is hard
Answer:
sin θ = (√21) / 5
tan θ = (√21) / 2
Step-by-step explanation:
Remember the formulas for the trigonometry ratios with SohCahToa:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
If cos θ = 2/5, then:
adjacent = 2
hypotenuse = 5
Remember all right triangles follow the Pythagorean Theorem. So if you are missing one side, you can solve.
Let's find the opposite side.
a² + b² = c²
2² + b² = 5²
4 + b² = 25
b² = 21
b = √21
opposite = √21
Now we know all three sides. Use the trigonometry ratios to find sine and tangent.
sin θ = opposite / hypotenuse
sin θ = (√21) / 5
tan θ = opposite / adjacent
tan θ = (√21) / 2
The dinner buffet offers a choice of 4 appetizers, 5 main courses and 4 desserts. How many possible appetizer-main course-dessert combinations are there? *
1 point
Step-by-step explanation:
The dinner buffet offers a choice of appetizers,main courses and desserts.
The number of appetizers available in the buffet = 4
The number of main courses available in the buffet = 5
The number of desserts available in the buffet = 4
By combinations, the possible appetizer-main course-dessert combinations are there in the dinner buffet = (4) (5) (4) = 80
How to get the inverse of this problem
Answer:
i think it is g(x)=x^3/8 -1
Step-by-step explanation:
Finding Coordinates of a Translation
Triangle XYZ has coordinates X(2, 4), Y(-3, 4), and Z(-3,1). If the triangle is translated using the rule
(x, y) → (x - 2, y + 1), what are the coordinates of Y'?
Y'(-5,5)
OY'(0,5)
Y'(-5,2)
Y'(-1,3)
Transformation involves changing the position of a shape
The coordinates of Y' are (-5, 5)
The vertices are given as:
X(2, 4), Y(-3, 4), and Z(-3,1)
The transformation rule is given as:
(x, y) → (x - 2, y + 1)
For vertex Y, we have:
(-3, 4) → (-3 - 2, 4 + 1)
Simplify
(-3, 4) → (-5, 5)
Hence, the coordinates of Y' are (-5, 5)
Read more about transformation at:
https://brainly.com/question/4289712
is 2 and 3/4 greater than 2 and 4/5
Answer:
no it is less then
Step-by-step explanation:
2 3/4 is equal to 2.75 in decimal form and 2 4/5 is 2.80 in decimal form so 2 3/4 is less the 2 4/5
Kaytlyn must build a sand castle in the form of a square pyramid for a project as shown to the left. She bought 3 bags of sand each containing 1200 inches cubed. Will she save enough sand to build the castle?
Answer:
see the explanation
Step-by-step explanation:
The complete question is
The dimensions of the square pyramid are
Base: 40 inches
Height: 12 inches
step 1
Find the volume of the square pyramid
The volume of the square Pyramid is given by the formula
[tex]V=\frac{1}{3}b^2h[/tex]
where
b is the length side of the square base
h is the height of the pyramid
we have
[tex]b=40\ in\\h=12\ in[/tex]
substitute
[tex]V=\frac{1}{3}(40)^2(12)[/tex]
[tex]V=6,400\ in^3[/tex]
step 2
Find the volume of sand
Multiply the number of bags of sand by the volume of each bag
so
[tex]3(1,200)=3,600\ in^3[/tex]
step 3
Compare the volume of the sand with the volume of the square pyramid
3,600 < 6,400
therefore
Kaytlyn has not enough sand to build the castle
What error did Amy make in writing the equation in slope-intercept form for the line shown in the graph?
Amy’s equation:
Answer:
letter C
Step-by-step explanation:
She substitue the X-Intercept, (3,0), for B
#brainliestisthekey