Answer:
try using the Pythagorean theorem
Step-by-step explanation:
hypotenuse ² = Opposite ² +Adjacent ²
where hypotenuse is the side facing the right angle sign;(x+3)
CARPENTRY A carpenter is building a podium. The side panel of the podium is cut from a rectangular piece of wood. The rectangle must be
sawed along the dashed line in the figure.
The measure of angle1 in the given rectangular figure is 64° .
In the question ,
it is given that ,
the one of the angle is 116° .
From the figure below ,
we can see that
the dashed line is a transversal to AB and CD ,
the angles on the line AB form a linear pair ,
So , angle2 + 116° = 180°
angle2 = 180° - 116°
angle2 = 64°
Since the side panel of the podium is cut from rectangular piece
the figure is representing two parallel lines , cut by the transversal .
By the property of transversal that alternate interior angles are equal in measure ,
angle 1 = angle 2
hence , angle 1 = 64° .
Therefore , The measure of angle1 in the given rectangular figure is 64° .
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what is the most appropriate measure of central tendency to use in determining the average time it takes students to graduate from college, assuming that a few students take an extraordinary long time to finish their degree, and why it is the most appropriate?
As a result of using all values in the data set to calculate an average, the mean is the most widely used measure of central tendency.
Why is central tendency important?A measure of central tendency, also known as a measure of center or a measure of central placement, is a summary statistic that seeks to summarize an entire collection of data by using a single number that corresponds to the middle or center of the distribution.
Where can you locate the central tendency?You are probably most familiar with the central tendency measure known as the mean, which is the arithmetic average. It is fairly easy to determine the mean. Simply add up all the values then divide by the dataset's observation count.
What use do central tendency metrics serve in evaluating student learning?The teacher can get a mathematical breakdown of how well the children are doing through measures of central tendency.
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bruce bought two books.one book costs $4 more than three times than the other.they both equal 72$
Bruce paid $17 and $55 respectively for each of the books
How to determine the cost of each book?From the question, we have the following statements:
Number of books = 2One book = $4 more than three times the other.Both books = 72$Represent the books with the variables x and y
So, we have the following equations
x = 4 + 3y
x + y = 72
To start with;
We can substitute 4 + 3y for x in the equation x + y = 72
So, we have the following representation
4 + 3y + y = 72
Evaluate the like terms
4 + 4y = 72
Collect the like terms in the above equation
So, we have the following equation
4y = 72 - 4
Evaluate the like terms
4y = 68
Divide both sides by 4
So, we have
y = 17
Recall that x = 4 + 3y
Substitute 17 for y in the equation x = 4 + 3y
x = 4 + 3 * 17
Evaluate the products
x = 4 + 51
Evaluate the sum
This gives
x = 55
Hence, the cost of the books are $17 and $55
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Possible question
Bruce bought two books, one book costs $4 more than three times than the other. They both equal $72.
What is the cost of each book
A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 peo
The number of days that the food will last when an average of 18 people are at the shelter everyday is 50 days.
How to calculate the number of people?From the information given, the shelter has enough food to feed an average of 45 hungry people a day for 20 days.
Let the number of days that the people can be fed when 18 people come be Illustrated as x.
Therefore, this will be illustrated as x. This will be:
x = (45 × 20) / 18
x = 900 / 18
x = 50
The number of days is 15 days.
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Complete question
A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 people are at the shelter everyday, how long will the food last?
A cycle Wheel does 1645 full turns in 7 minutes
work out the number of full turns per minute
The number of full turns per minute is 235.
Given that, a cycle Wheel does 1645 full turns in 7 minutes.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here,
The number of full turns per minute = Number of full turns/Number of minutes
= 1645/7
= 235 full turns per minute
Therefore, the number of full turns per minute is 235.
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It cost $4.50 for zoo parking, plus an additional $6.25 for admission per person into the zoo. If Jay starts off with $55.00 and buys 3 admission tickets, how much money will he have left?
Answer: he will be left with 31.74 dollars
Step-by-step explanation:
i first put 55.00 - 4.50 = 50.5
then you subtract 50.5 with 6.25 3 times so the and is 31.74
hope this helped !!
Eli is following this recipe to bake bread rolls.
He uses 900 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
600 g flour
12 g salt
9 g yeast
45 ml oil
360 ml water
g salt
0
g yeast
0
ml oil
0
ml water
Answer:
1022
Step-by-step explanation:
360+600+12+45+9=1022
Ms. Galindo’s class has adopted two equal sections of a highway to keep clean. The combined length of the two sections is
6/8
of a mile. How long is each section?
Each section of a highway has length of 1.5 miles.
In this question, Ms. Galindo’s class has adopted two equal sections of a highway to keep clean.
We need to find the length of each section.
Let each section measures x mile.
The combined length of the two sections is 6/8 of a mile.
So, we get an equation x + x = 6/8
We solve above equation to find the value of x.
2x = 6/8
x = (6/8) / 2
x = 6/4
x = 1.5
Therefore, each section of a highway has length of 1.5 miles.
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line that passes through the point (8,−3) and has a slope of 1/4
The equation of line having a slope of 1/4 which passes through point (8,-3) is y = (1/4)x - 5.
What is the equation of line with the given point and slope?The equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (8, -3 )
x = 8y = -3Slope m = 1/4Determine the y-intercept 'b'.
Substitute the point and slope into the equation of line formula and solve for b.
y = mx + b
-3 = (1/4)(8) + b
-3 = 8/4 + b
-3 = 2 + b
b = -3 - 2
b = -5
Now, substitute slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (1/4)x + (-5)
y = (1/4)x - 5
Therefore, the equation of the line is y = (1/4)x - 5.
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For each sequence, decide whether it could be arithmetic, geometric, or
neither.
1. 27, 9, 3, ...
2. 4, 8, 12,...
3. 50, 56, 60, ...
4. 36, 12, 4, ...
5. 4, 24,...
1. Therefore, the sequence is geometric.
2. Therefore, the sequence is arithmetic.
3. Therefore, the sequence is neither arithmetic nor geometric.
4. Therefore, the sequence is geometric.
5. Therefore, the sequence is neither arithmetic nor geometric.
Explain sequences and seriesFor the arithmetic, geometric, and harmonic sequences, a collection of sequences and series formulas is provided below. The sequence and series formulas presented here contain formulas for determining the sum of the n terms in a series as well as the nth term of the sequence.
A common difference exists between two succeeding terms in an arithmetic series. There is a typical ratio between succeeding terms in a geometric series.
1. Given sequence is 27, 9, 3, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{27}{9} = \frac{3}{3} = \frac{1}{3}[/tex]
Therefore, the sequence is geometric.
2. Given sequence is 4, 8, 12, ...
As we can see there is uniform difference of 4
Therefore, the sequence is arithmetic.
3. Given sequence is 50, 56, 60, ...
As the difference between the number is not uniform.
So, we will check for geometric sequence.
[tex]r = \frac{50}{56} \neq \frac{56}{60}[/tex]
There, the sequence is neither arithmetic nor geometric.
4. Given sequence is 36, 12, 4, ...
As the difference between the number is large.
So, we will check for geometric sequence.
[tex]r = \frac{36}{12} = \frac{12}{4} = 3[/tex]
Therefore, the sequence is geometric.
5. Given sequence is 4, 24, ...
The number of terms is very less and hence we can't decide.
There, the sequence is neither arithmetic nor geometric.
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Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on her original loan. At the end of 3 years she owes the bank $50,000. Since then, interest rates have increased to 12.75%. The bank will renew the mortgage at this rate, or Sandra can pay the bank $50,000. She decides to renew and will now pay $11.10 monthly per thousand on her loan. (You can ignore the small amount of principal paid during the 3 years.)
The old monthly payment is $
.
The new monthly payment is $
.
The percent increase in her monthly payment (to the nearest tenth) is
%.
The old monthly payment was = 9.27 x 50 = 463.5
The new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is 1.947%
Given,
Sandra Williams bought a home with a 10.25% adjustable rate mortgage for 25 years. She paid $9.27 monthly per thousand on his original loan
According to the question:
So, per thousand value of $65000 is 50000/1000 =50
Now, the old monthly payment was = 9.27 x 50 = 463.5
She decides to renew and will now pay $11.10 monthly per thousand on his loan.
So, the new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is= 11.10 /9.27 - 1 x 100
19.7411 % and to nearest tenth it is 1.947%
Hence, the old monthly payment was = 9.27 x 50 = 463.5
the new monthly payment is = 11.10 x 50 = 555
The percent increase in his monthly payment is 1.947%
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the probability that jacie will eat cheese on any given day is 0.6 while the probability that robyn will eat cheese on any given day is 0.25. if these events are independent, what is the probability that jacie or robyn will eat cheese on a randomly selected day?
The probability for Jacie or Robyn would consume cheese on a random day is 0.15.
What is defined as the independent events?Two occurrences are considered independent if indeed the occurrence of one does not alter the likelihood of the occurrence of the other. The mathematical expression of event independence A and B is the chance of both A and B occurring being equal to the sum of both the probabilities of both B and A (i.e., P) (A and B).The likelihood of Jacie eating cheese on any particular day is 0.6.
The likelihood of Robyn eating cheese on any particular day is 0.25.
Both events are independent.
As a result, the probability for Jacie or Robyn would consume cheese on a random day is;
P(Jacie or Robyn) = P(Jacie). P(Robyn)
P(Jacie or Robyn) = 0.6 x 0.25
P(Jacie or Robyn) = 0.15
Thus, the probability for Jacie or Robyn would consume cheese on a random day is 0.15.
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Use point-slope form to write the equation of a line that passes through the point
(1,-5) with slope-1.
The equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
Given:
(1,-5) with slope m = -1
The standard slope intercept form is y = mx + c.
substitute m = -1 and (1,-5)
-5 = -1(1) + c
-5 = -1 + c
c = -4.
y = mx + c
y = -1(x) + (-4)
y = -x - 4.
Therefore the equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
Therefore equation of a line that passes through the point (1,-5) with slope -1 is y = -x - 4.
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please help me with this problem.
Answer:
(- 25, 5 )
Step-by-step explanation:
- 3x - 6y = 45 → (1)
- 5y = x → (2)
substitute x = - 5y into (1)
- 3(- 5y) - 6y = 45
15y - 6y = 45
9y = 45 ( divide both sides by 9 )
y = 5
substitute y = 5 into (2)
- 5(5) = x , then
x = - 25
solution is (- 25, 5 )
Jerome tries to find the value of the expression 3 - 6 + 5 by first applying the commutative property. He rewrites the expression as 3 - 5 + 6. Explain, What is wrong with Jerome's approach?
The fault with Jerome's approach as required in the task content is; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.
What is the commutative property of addition?Commutative property of addition is a property of addition which posits that Changing the order of addends does not change the sum.
On this note, the use of the commutative property of addition on the given expression; 3 - 6 + 5 would yield the expression; 3 + 5 - 6.
Consequently, the fault with Jerome's approach is that; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.
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How many inches are in 5 1/4 feet?
Answer: 63 inches
Step-by-step explanation:
Answer:
63 inches
Hope this helps :)
mr. bray prepares a list of 434343 us presidents, 888 of whom died in office. then 181818 of his students each select a president at random (there can be repeats) for their creative writing assignments. what is the probability that at least one of the students select a president who died in office? round your answer to the nearest hundredth.
There is a 0.97541 or 97.541% probability that at least one student will choose a president who passed away in office.
Take into account the details offered.
43 US presidents are listed by Mr. Bray, 8 of them passed away while in office.
Consequently, p= 8/43.
If 8 of the 43 presidents died while in office, then 43-8=35 presidents survived.
q= 35/43
Let X represent how many presidents have passed away while in office.
The probaility that at least one student will choose a president who passed away in office is:
P(X[tex]\geq[/tex]1 ) = 1 -P(X=0)
P(X[tex]\geq[/tex]1 ) = 1 -¹⁸c₀(8/43)⁰(35/43)¹⁸
By using Combinations Formula,
By solving we get,
P(X[tex]\geq[/tex]1 ) = 0.97541
As a result, there is a 0.97541 or 97.541% chance that at least one student will choose a president who passed away in office.
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Graph the function f(x)=−14x−2.
Use the line tool and select two points to graph.
A bakery sells 4 dozen cupcakes every 3 hours. If the bakery is open 8 hours each day, how many days does it take to sell 640 cupcakes?
5 days does it take to sell 640 cupcakes.
Given:
A bakery sells 4 dozen cupcakes every 3 hours.
If the bakery is open 8 hours each day.
4 dozen cupcakes = 4*12 cupcakes
= 48 cupcakes
48 cupcakes = 3 hours
divide by 3 on both sides
3hours/3 = 48/3 cupcakes
1 hour = 16 cupcakes
Number of cupcakes for 8 hours = 8 * 16 = 128 cupcakes.
128 cupcakes sells in one day.
To sell 640 cupcakes = 640/128
= 5 days.
Therefore 5 days does it take to sell 640 cupcakes.
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
32 kg to 56 kg
Answer:
4/7
Step-by-step explanation:
32:56
32÷2=16
56÷2=28
16:28
16÷2=8
28÷2=14
8:14
8÷2=4
14÷2=7
4:7
32:56 ~ 32/56
=4/7
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he
has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.
a. What will the new principal be when he begins making loan payments?
b. How much interest will he pay over the life of the loan?
a) The new principal (principal + capitalized interest) when Rich begins making loan payments will be $9,425.10.
b) The total interest that Rich will pay over the life of the loan is $4,914.20.
How is interest on student loans determined?The interest on student loans is based on simple interest.
The only interest capitalized is the interest during the non-payment period if the student does not pay the interest.
Some students elect to pay the interest during the non-payment period to reduce the capitalized interest and principal during the payment period.
Capitalization refers to the addition of interest to the principal amount.
Period of student loan = 10 years
The amount of the federal unsubsidized student loan = $7,900
Interest rate = 4.29%
Capitalized interest during the non-payment time = $1,525.10 ($7,900 x 4.29% x 4.5)
New principal when Rich begins making loan payments = $9,425.10 ($7,900 + $1,525.10)
Total interest for loan = $4,914.20 ($7,900 x 4.29% x 14.5)
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Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Answer:
The answer is –3 < 1
Step-by-step explanation:
-3 is below zero. 1 is above zero. therefore, -3 less than 1
The radius of a circle is 599 cm. What is the diameter of this circle?
Answer:
1,198 cm
Step-by-step explanation:
To find the diameter, use the formula d = 2r.
d = 2(599)
d = 1,198
The length of KL¯¯¯¯¯¯¯¯ is 8x−17 units. The length of ST¯¯¯¯¯¯¯ is −2x+18 units. For what value of x are the segments congruent?
NO LINKS OR FILE
Answer:
x = 3.5units
Step-by-step explanation:
Congruent means the same length, so set the given lengths equal to each other.
8x - 17 = -2x + 18
Add 2x to both sides.
10x -17 = 18
Add 17 to both sides.
10x = 35
Divide by 10
x = 3.5
When x is 3.5, KL and ST are the same length. Check.
8(3.5) - 17 = 11
and
-2(3.5) + 18 = 11
ets
d and simplify these
4(a + 8) =
4(a + 8)
multiply out:
= 4a + 32
Warren has 40 coins (all nickels, dimes, and quarters) worth $4.05. He has 7 more nickels than dimes. How many quarters does Warren have?
Please provide a detailed explanation and steps on how to do
If he has 7 more nickels than dimes. The number of quarters that Warren have is 7.
How to determine the number of quarters?Let coins be:
n + d + q = 40
Where;
n = nickels
d =dimes
q = quarters
Hence,
.05n + .10d + .25q = 4.05
n = d + 7
Substitute (d+7) for n
(d+7) + d + q = 40
2d + q = 40 - 7
2d + q = 33
q = (33-2d)
So,
.05(d+7) + .10d + .25q = 4.05
.05d + .35 + .10d + .25q = 4.05
15d + .25q = 4.05 - .35
.15d + .25d = 3.70
Substitute (33-2d) for q
.15d + .25(33-2d) = 3.70
.15d + 8.25 - .5d = 3.70
.15d -.5d = 3.70 - 8.25
-.35d = -4.55
Divide both side by -/35d
d = -4.55 / -.35
d = 13 dimes
Nickels
n = d+7 where d is 13
n = 13 + 7
n = 20 nickels
Quarters
q = (33-2d)
q = 33 - 2(13)
q = 33 - 26
q = 7 quarters
Therefore 7 is the quarters.
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Karla drank a 15-fluid-ounce bottle of water before tennis practice. After practice, she drank 4 cups of water. What is the total amount of water Karla drank?
a 7 c and 9 fl oz
b 7 c and 7 fl oz
c 5 c and 9 fl oz
d 5 c and 7 fl oz
The total amount of water Karla drank before and after the tennis practice is 5 cups and 9 fluid ounces.
The correct answer option is option C.
What is the total amount of water Karla drank?Volume of water Karla drank before tennis practice = 15-fluid-ounceVolume of water Karla drank after tennis practice = 4 cupsConvert fluid ounces to cups:
1 fluid ounces = 0.125 cups
15 fluid ounces = 1.875 cups
Total volume of water Kayla drank = Volume of water Karla drank before tennis practice + Volume of water Karla drank after tennis practice
= 1.875 cups + 4 cups
= 5.875 cups
Approximately,
5 cups and 9 fluid ounces
Therefore, the total volume of water Karla drank is approximately 5 cups and 9 fluid ounce
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the student council at westford high school is making t-shirts to sell for a fundraiser, at a price of $10 apiece. the costs, meanwhile, are $6 per shirt, plus a setup fee of $72. selling a certain number of shirts will allow the student council to cover their costs. what will the costs be? how many shirts must be sold?
Cost will be $180 and so will be the revenue.
What is linear equation ?Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
CalculationCost: C=72+6s, where s is the number of shirts sold
Revenue: R=10s
Break-even is where they are equal
72 + 6s = 10s
72/4 = s
s = 18 shirt s
Cost will be $180 and so will be the revenue.
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How much of a radioactive kind of promethium will be left after 265 hours if the half-life is 53
hours and you start with 15,488 grams?
grams
Nick starts with 20
20
milligrams of a radioactive substance. The amount of the substance decreases by 12
1
2
each week for a number of weeks,
w
. He writes the expression 20(12)
20
(
1
2
)
w
to find the amount of radioactive substance remaining after
w
weeks.
Autumn starts with 1
1
milligram of a radioactive substance. The amount of the substance decreases by 50%
50
%
each week for a number of weeks,
w
. She writes the expression (1−0.5)
(
1
-
0
.
5
)
w
to find the amount of radioactive substance remaining after
w
weeks.
Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
Each part of Nick's and Autumn's expressions mean can be explained as follows;
Nick;
the amount of substance he begins with = 20the amount of substance left after each week = 1/2Autumn:
The one outside of parentheses = the initial amount of the substance.The one inside of parentheses = 100% of the original amount of the substance.0.5 represents the 50% of the substance that is lost each time periodHow to explain each variable in an expression?ler
Number of weeks = wNick expression:
[tex] {20( \frac{1}{2} })^{w} [/tex]
Where,
the amount of substance he begins with = 20
the amount of substance left after each week = 1/2
If w = 2
[tex] {20( \frac{1}{2} })^{w} [/tex]
[tex]{20( \frac{1}{2} })^{2} [/tex]
= 20(0.25)
= 5 milligrams
Autumn's expression:
[tex] {(1 - 0.5)}^{w} [/tex]
The one outside of parentheses = the initial amount of the substance.
The one inside of parentheses = 100% of the original amount of the substance.
0.5 represents the 50% of the substance that is lost each time period
If w = 2[tex] {(1 - 0.5)}^{w} [/tex]
[tex] {(1 - 0.5)}^{2} [/tex]
= (0.5)²
= 0.25 milligrams
Complete question:
Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 1/2 each week for a number of weeks, w. He writes the expression 20(12)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 1 milligrams of a radioactive substance. The amount of the substance decreases by 50% each week for a number of weeks, w. She writes the expression (1-0.5)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
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