The unite rate of the kendra's bike ride is found as 3 blocks / min.
Explain the meaning of the term unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with the number one as the denominator. A particular kind of ratio is a unit rate (or called a single-unit rate). One unit of one quantity will be compared to an unique number of units of another quantity.The given question is-
Total blocks covered = 30.Total time taken = 10 minutesUnit rate = number of blocks/ total time
Unit rate = 30 / 10
Unit rate = 3 blocks / min
Thus, the unit rate of the kendra's bike ride is found as 3 blocks / min.
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factorise xsquared-12x+27
Answer:
(x - 3) (x - 9)
Step-by-step explanation:
x² - 12x + 27
x² - 3x - 9x + 27
x(x - 3) - 9(x - 3)
(x - 3) (x - 9)
Thus, The answer is (x - 3) (x - 9)
A state seal, which is round, hangs in the capitol building. It has a radius of 2 yards. What is the seal's diameter?
Step-by-step explanation:
you do understand that the diameter of a circle is simply 2 times the radius, yes ?
imagine a circle and you draw a radius line (from the center of the circle to the circle arc).
and now imagine to draw another radius line, just in the opposite direction.
when you look at the result, you have 1 straight line going from the circle arc to the circle arc and passing through the center of the circle. that is what a diameter is.
how long is it ? well, we drew 2 radius lines to create this line. so, it is 2×radius long.
so, the diameter of the seal is
2×2 = 4 yards
Kristin's credit rating was lowered, and the credit card company raised her apr from 14% to 15. 2%. If her average daily balance this month is x dollars, express algebraically the increase in this month's finance charge due to the higher apr.
The algebraic expression for the increase in this month's finance charge due to higher APR is 0.001x .
In the question ,
it is given that ,
Kristin's credit rating was lowered ,
and the credit card company raised the APR from 14% to 15.2% ,
the average daily balance in this month is = $x .
the finance charge for 14% APR is = x*(14%/12)
= 0.01167x
the finance charge for 15.2% APR is = x*(15.2%/12)
= 0.01267x
So , the increase in finance charge is = 0.01267x - 0.01167x
= 0.001x
Therefore , the algebraic expression is 0.001x .
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∠c=?
a) 30° b) 50°
c) 70° d) 100°
∠c - ∠b =?
a) 30° b) 40°
c) 50° d) 70°
∠a=?
a) 80° b) 70°
c) 40° d) 30°
∠c = 100° (Since ∠c and ∠100° are opposite angles)
∠c - ∠b = 70° (∠b =30° since ∠b and ∠30° make 60°)
∠a = 30° (Since ∠a and ∠30° vertically opposite angles)
What are opposite angles?
Angles, where two lines cross that are directly opposite one another, are known as opposite angles. The vertex, where the lines come together to produce the angle, is the location of the junction. Vertical angles are another name for opposite angles. Congruent angles are those that have opposite angles that are equal or have the same measurement. For instance, A and C are referred to be opposite angles in the parallelogram ABCD. B and D are the opposing angles in a similar way.
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A cube with side length zzz has a volume of 216216216 cubic centimeters. The following equation shows the volume of the cube.
z^3 = 216z
3
=216z, cubed, equals, 216
What is the side length of the cube in centimeters?
Using the formula for volume of cube and with the provided volume and side, the answer is 6cm.
What is a cube?A cube is a three-dimensional solid object in geometry that is surrounded by six square faces, facets, or sides, three of which meet at each vertex.
What is the formula for volume of cube?We get the volume of a cube by thrice multiplying the side length.
Suppose we have a side length of cube = l cm
The required formula is for volume is:
[tex]V = l ^ {3}[/tex]
As per question, the side length of cube = z
l=z
V = z³
V=216 ³
[tex]l=\sqrt[3]{216}[/tex]
[tex]l=6cm[/tex]
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the initial population of a town is 100,231 and it grows with a doubling time of 98 years. what will the population be in 31 years?
If the initial population of a town is 100,231 and it grows with a doubling time of 98 years, the population after 31 years is 124803
The initial population of the town = 100231 people
The doubling time = 98 years
We have to find the population in 31 year
The exponential function will be
f(t) = fo(2)^(t/98)
f(t) is the population of the town in t years
fo is the population of the town in t = 0 years
t is the number of years
2 because it doubling time
The value of t = 31 years
Substitute the values in the function
f(31) = 100231×(2)^(31/98)
Do the arithmetic operations
f(31) = 100231 × 1.245
f(31) = 124803.23
f(31) ≈ 124803
Therefore, the population after 31 years is 124803
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which of the following represents 3 square root x^2 in exponential form?
Answer:
D
Step-by-step explanation:
the numerator of the exponent is the exponent of x
the denominator is the the index of the root
A graduate student is designing a research study. She is hoping to show that the results of an experiment are statistically significant. What type of p-value would she want to obtain?.
Answer: significant
Step-by-step explanation:
Your favorite basketball team has won 76% of the 50 games that they played so far this season. How many games has the
team won so far this season?
Answer:
38
Step-by-step explanation:
76% of 50 is 38
Answer: 38 games
Step-by-step explanation: The answer is actually pretty simple to get to. You just need to find 76% of 50. Let x be the amount of games they have won this year. The equation is: x= 0.76*50. Why it is 0.76 instead of 76 is because percent is always out of 100 that is why the max is 100%. So 0.76 is the same as 76/100 which is also 76%. Back to the equation: x = 0.76*50. If you solve the equation which is just 0.76*50, you would get 38. 38 is how many games they won in the season.
Morgan has 6 packs of erasers. Each pack of erasers has x erasers in it. After Avery gives her 3 more erasers, she has a total of 27 erasers.
a. Model the situation with an equation.
b. Find a solution to your equation from part (a)
c. Interpret the solution in the context of the problem.
Answer:
a.6x+3=27
b.x=4
c. Morgan has 6 packs of erasers, each pack has 4 erasers, and after Avery gives her three more erasers, she has a total of 27.
Step-by-step explanation:
a.6x+3=27
6x=24
b.x=4
c. Morgan has 6 packs of erasers, each pack has 4 erasers, and after Avery gives her three more erasers, she has a total of 27.
imran s father is 50 years old and Imran is 2 years old now . how many years ago was Imran s father was three times as old as him
Answer:
25
solution
50=3x
or, 50/3=x
or, x=16.66
hence,imran father will 16 years
Sam is filling up his pool. The water hose filled the 288 gallon pool in 48 minutes. At what rate did the hose fill the pool in gallons per minute?
At 6 gallons per minute, the hose moves water.
How long does it take to fill a pool with a hose?The hose is the first thing most people think of, and if you are extremely patient, have several hoses, and are not utilizing well water, that is a workable alternative. Even with a few hoses running, it can take 12 to 24 hours to fill an average pool.Example :Our tutors' response was given
X gallons per minute is what we'll suppose the hose can provide.
288 : 48 = x : 1
x = 288/48
x = 6 gal/min.
At 6 gallons per minute, the hose moves water.
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If I was born in 2008, how many years do I need to be 18?
Answer:
4 more years
Step-by-step explanation:
you were born in 2008, you should be 14 now or soon, by the end of the year. So 4 in 4 years you would be 18.
Answer: Simple, you are 14 right? So 4 more years
Step-by-step explanation:
Add 14+4 and you'll get 18.
Find an explicit formula for the following equence, an which tart with a1=23. 23,34,45,56,…
The explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11. Here the first term is a1 = 23 and the common difference is d = 11.
What is the explicit formula for an arithmetic sequence?The explicit formula for an arithmetic sequence gives the nth term of the sequence. I.e.,
aₙ = a1 + (n - 1)d
Here a1 is the first term; d is a common difference, it is calculated by
d = aₙ₊₁ - aₙ = aₙ₋₁ - aₙ
Calculation:The given sequence is 23, 34, 45, 56,...
Here the first term a1 = 23
So, the common difference between the terms in the sequence is
d = 34 - 23 = 11
Then, the explicit formula for the given sequence is
aₙ = a1 + (n - 1)d
⇒ aₙ = 23 + (n - 1)11
Therefore, the nth term of the explicit formula for the given arithmetic sequence is aₙ = 23 + (n - 1)11.
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2.5kg of potatoes cost £1.40
Work out the cost of 4.25g of potatoes
The cost of 4.25 grams of potatoes is £0.00238
How to determine the cost of 4.25 grams?From the question, we have the following parameters that can be used in our computation:
2.5kg of potatoes cost £1.40
This means that the unit rate can be calculated as
Unit rate = Cost/Amount
So, we have the following representation
Unit rate = 1.40/2.5
The cost of 4.25 grams is calculated as
Cost = Unit rate * Amount
So, we have the following representation
Cost = 4.25 * 1.40/2.5
Convert to grams
Cost = 4.25 * 1.40/2500
Evaluate
Cost = 0.00238
Hence, the cost is 0.00238
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the sum of two consecutive if the first one is n
Step-by-step explanation:
The sum of two consecutive integers if n is the first integer.
consecutive means immediately after, so we have:
n
n + 1
The sum is written as:
n + n + 1
Grouping like terms, we have:
(n + n) + 1
2n + 1
Which of the following equations is correct? Select all that apply.
Answer:
option a is correct i.e 6.25 = 25/4
Step-by-step explanation:
= 6.25
= 625 / 100
both being divisible by 5
we get
= 25/4
 Write an equation in slope-intercept form of the line that is parallel to the one given and passes through the given point
(1,3); y=7x+5
An equation in slope-intercept form of the line that is parallel to the one given and passes through the given point is y=7x+5.
x - axis interception points of [tex]$7 x+5: \quad\left(-\frac{5}{7}, 0\right)$[/tex]
y - axis interception point of [tex]$7 x+5: \quad(0,5)$[/tex]
X-Intercepts: [tex]$\left(-\frac{5}{7}, 0\right)$[/tex], Y Intercepts: (0,5)
Slope of [tex]$7 x+5: \quad m=7$[/tex]
Steps
7x+5
What is line equation?
For a line equation for the form of y=m x+b, the slope is m. m=7
The first step to answering this question is to find the slope of the first line. To do that, we need to put it in slope-intercept form.
y=7x+5 => y=7x+5
So the slope of this line is 7. Perpendicular lines have a negative reciprocal slope, so the slope of the perpendicular line is 7. Using that and the point (1,3) we can make an equation for the line in point-slope form: We can then convert this into slope intercept form.
=> y=7x+5
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29% of all telephones of a certain type are submitted for service while under warranty. of these, 51% can be repaired whereas the remaining must be replaced under warranty. if a company purchases 10 of these telephones, what is the probability that exactly 2 will end up being replaced under warranty? (state your answer in decimal terms precise to three decimal places.)
Probability that exactly 2 will end up being replaced under warranty is 0.14781.
The problem states that 20% are likely to need warranty service, and of the 20% that need repair, 40% are likely to need to be replaced. This implies that 8% of the total are likely to need warranty service and be replaced (.20)(.40)=0.08
Therefore, p=0.08
n=10
and x=2 then we have to put the values in the formula,
We now plug all of this into formula , then we get
b(x;n,p) = [tex]\left \{ {{n} \atop {x}} \right. }px(1-p) to the power n-x\\[/tex]
and we get ,
So,
b(2;10,0.08) = (10 2)(0.08)²(1-0.08) to the power 10-2
=45(0.0064)(0.92)to the power 8≈0.14781
So, the probability is 0.14781
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You have a $40 coupon and a 10% off
promotional dicount for a limouine rental. The cot
of the limouine i $100 per hour, plu a 20% gratuity. You rent the limouine for 4 hour. Ue compoition
of function to find the amount you pay in each
ituation. A. The coupon i applied before the promotional
dicount. B. The promotional dicount i applied before
the coupon
When we apply coupon before promotional discount, we have to pay $396.
When we apply promotional discount first and then coupon, we have to pay $392
Given,
The coupon amount = $40
Promotional discount = 10%
The rent per hour = $100 + 20% gratuity
The rent for 4 hours including gratuity = (100 × 4) + (100 × 4 + 10/100) = $480
We have to find the amount for the situations given below;
a) The coupon is applied before the promotional discount;
Here,
Coupon deduction;
480 - 40 = $440
Promotional discount deduction;
10% of 440 = 44
Then,
440 - 44 = $396
We have to pay $396.
b) The promotional discount is applied before coupon;
Here,
Promotional discount deduction;
10% of 480 = 48
Then,
480 - 48 = $432
Coupon deduction;
432 - 40 = $392
We have to pay $392.
Therefore,
When we apply coupon first and then promotional discount, we have to pay $396
When we apply promotional discount before coupon, we have to pay $392.
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What are the vertex and range of y = |x − 5| + 4?
(5, 4); −∞ < y < ∞
(5, 4); 4 ≤ y < ∞
(−5, 4); −∞ < y < ∞
(−5, 4); 4 ≤ y < ∞
The vertex and the range of y = |x - 5| + 4 are (b) (5, 4); 4 ≤ y < ∞
How to determine the vertex and the range?The equation is given as
y = |x - 5| + 4
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
This means that the vertex is
Vertex = (5, 4)
Remove the x value
y = 4
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 4
So, the range is 4 ≤ y < ∞
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Answer: I think C
Step-by-step explanation:
Which expression is equivalent to x + x + x + x?
Step-by-step explanation:
4x is the equivalent expression if thats an option
A company makes two chemicals: Type I and Type II. Due to storage problems, a maximum of 100 pounds of Type I and 150 pounds of Type II can be mixed and packaged each year. One pound of Type Itakes 62 hours to mix and 78 hours to package; one pound of Type II takes 44 hours to mix and 46 hours
to package. The mixing department has at most 7220 hours available each year, and packaging has at most 8260 hours available. If the profit for one pound of Type I is $70 and for one pound of Type II is $46, what is the maximum profit possible each year?
Max profit would be 54 type 1 and 88 type 2
what is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
given:
Let x be the amt of type 1 and y be the amt of type 2.
Then, Storage constraints
x ≤ 100
y ≤ 150
and, Mixing constraint:
62x + 44y ≤ 7220
44y = 7220-62x
y = 164 - 1.4x
and, Packaging constraint:
78x + 46y ≤ 8260
46y = 8260 - 78x
y = 180 - 1.7 x
Then, The objective functions for each corner of the region
solve:
62x + 44y = 7220
78x + 46y = 8260
So, x=54,y=88
Hence, Max profit would be 54 type 1 and 88 type 2
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The yearly profits of a company is $25,000. The profits have been decreasing by 6% per year. Write an exponential function that represents this scenario.
Answer: taxes
Step-by-step explanation:
Cozy nights industries manufactures down-filled comforters and uses activity-based costing. The following information is provided for september. Activity estimated indirect activity costs allocation base estimated quantity of allocation base materials handling $ 12,600 number of parts 4,200 parts assembly 55,440 number of parts 4,200 parts packaging 10,920 number of comforters 1,050 comforters each comforter consists of 4 parts and the direct materials cost per comforter is $14. 0. Based on the information given for cozy nights industries, what is the total cost of packaging each comforter?.
The required total cost of packaging each comforter is $89.20.
How to calculate the total cost of packaging each comforter?Activity estimated indirect activity costs allocation base estimated quantity of allocation base,
materials handling $ 12,600 number of parts 4,200 parts
Cost per part = $ 12,600/4,200 = $3
assembly$ 55,440 number of parts 4,200 parts,
Cost per part = $ 55,440/4,200 = $13.20
packaging $10,920 number of comforters 1,050 comforters each comforter consists of 4 parts
Cost per part =$10,920 /1,050 = $10.40
Then, For all cost of 4 parts,
Materials handling = ($3 x 4) = $12
Assembly = ($13.20 x 4) = $52.80
Packaging = ($10.40 x 1) = $10.40
Total overhead cost = $75.20
And Direct materials cost = $14.00
So, total manufacturing cost = $75.20 + $14.00 = $89.20
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Lillian has a rectangular garden with an area of 10x2 +33x – 7 square feet. Find the expressions that would represent the length and width of the garden. Make sure you show all your work for full credit.
Attempt was made but incorrect
(1 pt)
Correct but no work shown OR less than half the work is correct
(2 pts)
About half of the work is correct
(3 pts)
Most of the work is correct (4 pts)
Fully Correct with all work shown
(5 pts)
If Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that, Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet.
We have to find the expression representing the length and width of the garden.
[tex]=10x^2+33x-7 \\\\ =\left(10x^2-2x\right)+\left(35x-7\right) \\\\ =2x\left(5x-1\right)+7\left(5x-1\right)\\\\ =\left(5x-1\right)\left(2x+7\right)[/tex]
The area of the rectangular garden is,
A = L × B
Comparing the expression with the obtained expression we get the expressions that would represent the length and width of the garden as,
A= (5x-1)(2x+7)
Thus, if Lillian has a rectangular garden with an area of 10x² +33x – 7 square feet. The expressions that would represent the length and width of the garden will be (5x-1)(2x+7)
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A department store buys 200 shirts at a cost of $2,400 and sells them at a selling price of $20 each. Find the percent markup.
If the store buys 200 shirts for $2400 and sells for $20 each then the percent markup is = 66.67% .
In the question ,
it is given that ,
the number of shirts that departmental store buys is = 200 shirts .
the cost price for 200 shirts is = 2400
So , the cost for 1 shirts is = 2400/200 = $12 ,
the selling price for 1 shirt is = $20 ,
the percent markup can be calculated using the formula ,
percent markup = (selling price - cost price)/(cost price) × 100 ,
= (20 - 12)/12 × 100
= 8/12 × 100
= 800/12
= 66.66666
≈ 66.67 % .
Therefore , percent markup is 66.67% .
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The ratio of the number of girls to the number of boys was 2 to 5. If 2,450 students were present, how many were girls and how many were boys? (hint: try using a proportion to solve)
Girls =
Boys =
The number of boys were 1750 boys and the number of girls were 700 girls .
In the question ,
it is given that ,
the ratio of the number of girls to the number of boys is 2 : 5.
So , the number of boys is = 5x
and the number of girls is = 2x ,
also given that , the total number of students is = 2450
So , According to the question ,
5x + 2x = 2450
7x = 2450
Dividing both sides by 7 ,
we get ,
x = 2450/7
x = 350 ,
Hence , the number of girls = 2(350) = 700
and the number of boys is = 5(350) = 1750 .
Therefore , there are 700 girls and 1750 boys .
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What is the value of x? Please give steps on how you did it. Please, Hurry it is due at 11:59 pm.
Answer:
51/3
Step-by-step explanation:
Angles opposite congruent sides of a triangle are congruent.
[tex]x+17=4x-34 \\ \\ 17=3x-34 \\ \\ 51=3x \\ \\ x=51/3[/tex]
15 POINTS
Determine the perimeter of the right triangle shown.
right triangle with vertices at negative 4 comma 4, 4 comma 4, and 4 comma negative 2
10 units
24 units
36 units
64 units
The perimeter of the triangle is 24 units.
What is a triangle?
Triangle is bounded area by three sides. If length of all sides is not equal, then the triangle is known as an obtuse triangle.
The vertices of the triangle are A(-4,4), B(4,4), and C(4,-2)
The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²]
The length of line segment AB is √[(4 - (-4))² + (4 - 4)²] = √8² = 8 units
The length of line segment BC is √[(4 - 4)² + (-2 - 4)²] = √6² = 6 units
The length of line segment AC is √[(4 - (-4))² + (-2 - 4)²] = √[8² + 6²] = √100 = 10 units.
The perimeter of a triangle is sum of all sides of the triangle.
The perimeter of the triangle is
AB + BC + AC
= 8 + 6 + 10
= 24 units
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