When speed and time are known, distance can be calculated using the formula 'distance = speed x time'. Given Bert's speed of 50 mph and travel time of 0.5 hours each way, the distance from his home to the office is calculated to be 25 miles.
Explanation:The subject of this problem is fundamentally about understanding the relationship between speed, time, and distance. In this particular case, Bert is spending a total of an hour commuting to and from office. However, this total time includes both the journey to work and the journey back home so each journey takes half an hour or 0.5 hours. Given that his average speed is 50 mph, we can calculate the distance he travels one way using the formula "Distance = Speed x Time."
So, for Bert:
Distance = 50 mph x 0.5 hours = 25 miles
Therefore, "Bert lives 25 miles from his office."
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What are the dimensions of the rectangle shown on the coordinate plane? On a coordinate plane, a rectangle has points (1, -1), (10, -1), (10, -5), (1, -5). The base is 3 units and the height is 9 units. The base is 9 units and the height is 4 units. The base is 10 units and the height is 4 units. The base is 11 units and the height is 6 units.
The dimensions of the rectangle shown on the coordinate plane is The base is 9 units and the height is 4 units.
Option: B.
Step-by-step explanation:
We are given with the coordinate points of a rectangle.
The points are (1, -1), (10, -1), (10, -5), (1, -5).
From the given graph, the bigger side is the base and the height is the smaller side.
The points (1, -1), (10, -1) and (1, -5), (10, -5) can be used to find the base of the rectangle.
The points (10, -1), (10, -5) and (1, -1), (1, -5) can be used to find the height of the rectangle.
Let us find the base using coordinate point (1, -5), (10, -5) .
Since the base runs horizontally on the x-axis, we have to find the run.
run = [tex]x_2-x_1[/tex].
run = 10-1.
run (base)= 9 units.
Let us find the base using coordinate point (10, -1), (10, -5) .
Since the height runs vertically on the y-axis, we have to find the rise.
rise = [tex]y_2-y_1[/tex].
rise = -5-(-1).
rise=-5+1.
rise (height)= 4 units. ( Units are always measured in positive.)
∴ The base is 9 units and the height is 4 units.
10. Calculate 18% of 75 to one decimal place.
First write 18% as a decimal by moving the decimal point two places to the left to get .18.
The word "of" means multiply, so we have (.18)(75) which is 13.5.
Answer:
13.5
Step-by-step explanation:
18% of 75
18% /100% x 75
0.18 x 75
13.5
how to solve 3(x+4)-2(x+4)
Answer:
1.Distribute values
(3x+12)-(2x+8)
2.Add common terms
x+4
A bakery uses ounces of icing for every of a cake. What is the unit rate in ounces of icing per cake?
A.
ounces of icing per cake
B.
ounces of icing per cake
C.
ounces of icing per cake
D.
ounces of icing per cake
Answer:
Here is a similar question:
A bakery uses 10 1/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake.
The unit rate in ounces of icing per cake = 40 4/5 ounces
Step-by-step explanation:
Given:
Ounces of ice used for every 1/4 cake = 10 1/5
We have to find the unit rate.
Let the unit rate be 'x' .
Unit rate is the rate when we use unit 'one' as our reference to find any value.
Lets convert the mixed fraction of ounces.
⇒ [tex]10\frac{1}{5} = \frac{(10\times 5)+1}{5} =\frac{51}{5}[/tex]
Portion of the cake used = [tex]\frac{1}{4}[/tex]
To find the unit rate here we must divide :
⇒ [tex]x=\frac{number\ of\ ounces\ used}{portion\ of\ the\ cake}[/tex]
⇒ [tex]x=[/tex] [tex]\frac{51}{5}[/tex] ÷ [tex]\frac{1}{4}[/tex]
⇒ [tex]x=[/tex] [tex]\frac{51}{5}\times \frac{4}{1}[/tex]
⇒ [tex]x=[/tex] [tex]\frac{51\times 4}{5}[/tex]
⇒ [tex]x=[/tex] [tex]\frac{204}{5}[/tex]
⇒ [tex]x=[/tex] [tex]40\frac{4}{5}[/tex] Or [tex]40.8[/tex]
Hence, the unit rate in ounces of icing per cake = 40 4/5 ounces.
Answer:
Another similar question:
A bakery uses 10 3/5 ounces of icing for every 1/4 of a cake. What is the unit rate in ounces of icing per cake?
Step-by-step explanation:
Answer is 42 2/5
10 3/5 ÷ 1/4 = 53/5 ÷ 1/4
= 53/5 x 1/4
= 212/5
= 42 2/5
Increase 750 g by 20%.
Answer:
900 g
Step-by-step explanation:
Increase by 20% means 120% of the value
120/100 × 750
900g
Your credit score is 580. Your current credit card limit is $2,000. Your current credit card balance is $1,950. If you shrink your debt balance by 13% each month for 12 months what will your balance be?
Answer:
$366.66
Step-by-step explanation:
You start with a credit card balance of $1950. If you reduce this balance by 13% each month for 12 months, using the formula for geometric series (a(r^n)), your final balance at the end of 12 months will be approximately $452.98.
Explanation:The student's question is asking about reducing a credit card debt balance by a fixed percent each month. In this case, the student is reducing their debt by 13% every month for 12 months. To get a clear picture, let's go through this step by step.
Initially, the credit card balance is $1950. In the first month, the student reduces the debt by 13% which is $253.5. So, the remaining balance at the end of first month would be $1950 - $253.5 = $1696.5
This process is repeated each month. For example, in the second month, the student reduces the new amount of $1696.5 by 13%. The debt will continue to decrease in this manner each month.
To calculate the balance at the end of 12 months, we would use the formula for geometric series: a(r^n), where 'a' is the initial amount of debt($1950), 'r' is the percentage (1 - 13% or 0.87) and 'n' is the number of months (12).
Your final balance at the end of 12 months would be $1950*(0.87^12) which approximately equals $452.98. Hence, by reducing your debt by 13% each month for 12 months, your balance will be approximately $452.98. But remember, maintaining steady payments and not adding to the balance by new purchases is also important in managing credit card debt.
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please help i will mark brainliest 50 points
Mr. Wilson is giving his students a vocabulary test tomorrow over all the terms they have learned from this semester. Today, he wants to determine how prepared the students are for the test. So, he writes each term on a note card and puts all the note cards in a paper bag. Then, he asks each student to come to his desk, select five note cards out of the bag, define those five terms, and then put the note cards back in the bag. He records the number of terms each student is correctly able to define.
What is the population in this situation? What is the sample? Use complete sentences in your answer.
Do you think the data from the sample Mr. Wilson is collecting is representative of the population? Explain your reasoning using complete sentences.
The population in this situation is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag.
Explanation:
The population in this situation of Mr Wilson is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag. The sample is every set of 5 note cards that is selected by the students.
The data is representative of the population because they are selected randomly without bias. Every of term has the same probability of being selected. Also it given that the cards are replaced every time, so all the students will face the same population when they are going to select a sample.
Fully simplify. −3x2y5(5x5y4)-3x^2y^5(5x^5y^4) −3x 2 y 5 (5x 5 y 4 )
To add 547+ 327, would you need to regroup ?
Answer:
yes
Step-by-step explanation:
when addi g the ones place it would result in 14 so u would need to regroup the 1 into the tens place
(12 – 8)3 – 24 x 2
Evaluate the expression
• Determine the coordinates of the vertices of the rectangle to compute the area of the rectangle using the distance formula (round
to the nearest integer).
A) 35units B) 50units C) 60units D) 70units
Answer:
the correct answer is d
Step-by-step explanation:
The Area of rectangle is 30 sq. unit.
What is Distance Formula?The distance between two points A( a,b) and B(c, d) in coordinate plane is
D= √(c- a)² + (d- b)²
Given:
From the figure the coordinates of rectangle are A(3, 8), B(6, 11), C(11, 6) and D(8, 3).
Using Distance Formula
length: l = √(8-3)² + (3-8)² = √25 + 25 = √50
width: w= √(6-3)² + (11- 8)² = √9+9 = √18
So, the area of rectangle = l x w
= √50 x √18
= √50 x √18
= √900
= 30 sq. unit.
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As, the Questions figure is not given. So, this question is solved with different figure but with same method of solving.
2/5 with an exponent of 3
Answer:
2/5 with an exponent of 3 is 8/125 or 0.064
Step-by-step explanation:
Given:
A fraction = 2/5
Exponent = 3
To find the value of the fraction using the exponent.
We know that :
⇒ [tex](a)^3=a\times a\times a[/tex]
The exponents is the number of times a number is multiplied.
So,
⇒ [tex](\frac{2}{5})^3[/tex]
⇒ [tex]\frac{2\times 2\times 2}{5\times 5\times 5}[/tex]
⇒ [tex]\frac{8}{125}[/tex]
On further division the number can be written as 0.064
What is 4c + 8c = -55 + 3c
To solve this, you need to isolate/get the variable "c" by itself in the equation:
4c + 8c = -55 + 3c You can first combine like terms (4c and 8c)
12c = -55 + 3c Subtract 3c on both sides
9c = -55 Divide 9 on both sides
[tex]c=-\frac{55}{9}[/tex]
Given f(x) = x² + 8x and g(x) = x4, choose
the expression for (fºg)(x).
The expression for the new function (fog(x)) = x⁸ + 8x⁴
What is a composite function?
A composite function some called function of a function is a process whereby two functions produce a third function.
Let assume there is a function f(x) and g(x), a composite function fog(x) read as f of g of x, produces a third function h(x).
In the given question, we are to find (fog) (x), we will replace the value of the function g(x) for x in f(x).
i.e.
f(g(x) = x² + 8x
[tex]f(g(x) = (x^4)^2+8(x^4)[/tex]
[tex]f(g(x)) = x^8+8x^4[/tex]
A rectangular bathroom floor is covered with square tiles that are 1 1/2 feet by 1 1/2 feet. The length of the bathroom floor is 10 1/2 feet and the width is 6 1/2 feet
Answer:
The number of square tiles required to cover the bathroom floor is approximately 31.
Step-by-step explanation:
The dimensions of the rectangular floor of the bathroom are:
Length = 10.5 ft.
Breadth = 6.5 ft.
The dimensions of the square tiles are:
Side = 1.5 ft.
The area of the rectangular floor of the bathroom is:
[tex]Area\ of Bathroom\ floor=Length\times Breadth\\=10.5\times6.5\\=68.25[/tex]
The area of 1 square tile:
[tex]Area\ of\ 1\ square\ tile=(SIde)^{2}\\=(1.5)^{2}\\=2.25[/tex]
The number of tiles required to cover the bathroom floor is:
[tex]Number\ of\ tiles=\frac{Area\ of\ bathroom\ floor}{Area\ of\ 1\ square\ tile} \\=\frac{68.25}{2.25}\\ =30.3333\\\approx31[/tex]
Thus, the number of square tiles required to cover the bathroom floor is approximately 31.
Multiply the algebraic expression using a Special Product Formula and simplify.
(x − 7y)^2
The simplified expression is x^2 - 14xy + 49y^2.
To multiply the expression (x - 7y)^2 using the Special Product Formula, we can use the formula (a - b)^2 = a^2 - 2ab + b^2.
In this case, a = x and b = 7y. Plugging these values into the formula, we get:
(x - 7y)^2 = x^2 - 2(x)(7y) + (7y)^2
Simplifying further:
= x^2 - 14xy + 49y^2
So, the simplified expression is x^2 - 14xy + 49y^2.
Which equation best describes the graph of the line that has slope-1/3 and passes through point
(3.-9)?
Answer:
y=-1/3x-8
Step-by-step explanation:
y-y1=m(x-x1)
y-(-9)=-1/3(x-3)
y+9=-1/3x+3/3
y+9=-1/3x+1
y=-1/3x+1-9
y=-1/3x-8
PLZZZ HELP ASAP!!!!! Part A: Explain how to write an equivalent expression for 3(4x + 2) using the distributive property. Part B: Prove the 2 expressions are equivalent by substituting x = 2 into both expressions. *
3(4x + 2)
= 3 . 2(2x + 1)
= 6(2x + 1)
proof
• 3(4x + 2)
= 3(4(2) + 2)
= 30
• 6(2x + 1)
= 6(2(2) + 1)
= 30
Find the final price on a $1049 television that is on sale for 12% off if the sales tax is 4.5%
The final price of a $1049 television on a 12% sale, with a 4.5% sales tax, is $964.66.
Explanation:The final price on a $1049 television that is on sale for 12% off can be found by deducting the discount from the original price, and then adding the sales tax on the discounted price.
First, let's find the discount: 12% of $1049 is (12/100)*1049 = $125.88. So, the price after discount would be 1049 - 125.88 = $923.12.
Next, we need to add the 4.5% sales tax. Sales tax is calculated on the discounted price, so 4.5% of $923.12 is (4.5/100)*923.12 = $41.54.
Finally, we add the tax to the discounted price to get the final price: $923.12 + $41.54 = $964.66. So, the final price of the television is $964.66.
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Use properties of rational numbers to multiply the following.
6/7 x 42.21
Step-by-step explanation:
We have,
[tex]\dfrac{6}{7} \times 42.21[/tex]
To find, the value of [tex]\dfrac{6}{7} \times 42.21[/tex] = ?
∴ [tex]\dfrac{6}{7} \times 42.21[/tex]
= [tex]\dfrac{6}{7} \times \dfrac{4221}{100}[/tex]
We know that,
The properties of rational numbers,
[tex]\dfrac{a}{b} \times \dfrac{c}{d} =\dfrac{a\times c}{b\times d}[/tex]
= [tex]\dfrac{6\times 4221}{7\times 100}[/tex]
= [tex]\dfrac{25326}{700}[/tex]
= 36.18
Thus, the value of [tex]\dfrac{6}{7} \times 42.21[/tex]= 36.18
What is 1 1/3 times 1 4/9 in fraction form
Answer:
52 / 27
Step-by-step explanation:
To multiply mixed numbers, convert them into improper fractions. Multiply the two improper fractions together and simplify the result.
Explanation:To multiply mixed numbers, we first convert them into improper fractions. To convert 1 1/3 into an improper fraction, we multiply the whole number (1) by the denominator (3) and add the numerator (1). This gives us 4/3. Similarly, to convert 1 4/9 into an improper fraction, we multiply the whole number (1) by the denominator (9) and add the numerator (4). This gives us 13/9.
Now, we can multiply the two improper fractions together. 1 1/3 times 1 4/9 equals (4/3) * (13/9). To multiply fractions, we multiply the numerators together and multiply the denominators together. So, (4/3) * (13/9) equals (4 * 13) / (3 * 9), which simplifies to 52/27.
Therefore, 1 1/3 times 1 4/9 in fraction form is equal to 52/27.
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Please give me the answer and explain how you got it.
The measure of m∠KPN is 68°.
Step-by-step explanation:
From the given diagram, we are given with lines passing through a point P creating different angles.
Data given,
m∠KPN = 4x°.
m∠NPO = (x+5)°.
And m∠KPO= 90°.
The m∠KPO is spitted into m∠KPN and m∠NPO.
Thus the sum of m∠KPN and m∠NPO will be m∠KPO.
⇒m∠KPN + m∠NPO =m∠KPO.
Substitute the values to find x value.
4x°+(x+5)°= 90°.
(°5x+5)=90°.
5x°=90°-5°.
5x°=85°.
x=[tex](\frac{85}{5} )[/tex].
x= 17.
⇒m∠KPN = 4x°.
=4(17)°.
m∠KPN =68°.
Thus the measure of m∠KPN is 68°.
The product of 6.3 and g increased by 14
Answer:
Step-by-step explanation:
6.3g + 14
Answer:
6.3g + 14
Step-by-step explanation:
Help please!!! Show how you go the answer too
Answer:
Step-by-step explanation:
If QPS is a right angle we know a right angle equals 90 degrees. so you can find your answer by doing 90-35.
Therefore getting 56.
Hope this helps :)
how do you get b? show me how if you can, please.
Answer:
<ABC = 98.
Step-by-step explanation:
We know that the triangle is lying on a flat line, which is 180 degrees. We know that angle ABC and angle CBD are supplementary as they both use line ABD as their transversal.
Set up the equation (3 + 5x) + 82 = 180.
Solve for x, and you get 19.
Plug it back in to (3 + 5x), we get <ABC = 98.
Ami is having a pizza party on Saturday night. She ordered 8 pizzas. If the average person eats 1/3 of a pizza, how many persons will 8 pizzas serve
Answer:
The answer is 24
Step-by-step explanation:
If each person eats 1/3 of the pizza then that means it takes 3 people to eat a whole pizza so you multiply three times 8 and you get twenty four.
I WILL MARK BRAINLIEST TO WHOEVER GETS IT FIRST.
Convert 2000 ft per minute to miles per hour. Round to the nearest tenth.
Answer:
22.7
Step-by-step explanation:
A pot of boiling water at 212 degrees Fahrenheit on the stove has less thermal energy than a hot tub full of water at 100..4 degrees. true or false
Answer:
False
Step-by-step explanation:
Whichever has more heat (in this case the stove) has more thermal energy
Which of the following linear equations has the steepest slope?
Answer:
D
Step-by-step explanation:
Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. Find the measure of each angle
15° and 165°
Step-by-step explanation:
Step 1 :
Let x and y denote the angles with x as the smaller angle and y as the larger angle
When 2 angles are supplementary, the sum of both the angles is 180 degrees.
Hence x + y = 180
Step 2:
Given that the larger angle is 15 more than 10 times the smaller angle
Hence y = 15 + 10 x
Step 3 :
Solving for the 2 equations we have
11x = 165 => x = 15
=> y = 180-15 = 165
Hence the 2 angles are 15 and 165 degrees.