Answer:
x = 62
Step-by-step explanation:
40 + (x + 16) + x = 180 (sum of angles in a triangle=180)
2x + 56 = 180
2x = 124
x = 62
Last Friday, Kira and Marcy got dinner at Seaside Sushi restaurant. Kira ordered 2 pieces of tuna and 5 pieces of crab. Marcy ordered 3 pieces of tuna and 6 pieces of crab. Did Kira and Marcy order the same ratio of tuna pieces to crab pieces?
Answer:
no
Step-by-step explanation:
because Kira ordered 5 pieces of crab while Marcy has ordered 6 pieces of crab
81 to the 5th power = 3x
x=?
The value of x according to the given equation as in the task content is; 3¹⁹.
What is the value of x according to the given expression?It follows from the task content that the value of x is to be determined from the equation given in the task content.
Therefore, since the equation given in the task content is;
(81)⁵ = 3x
(3⁴)⁵ = 3x
3²⁰ = 3x
Therefore, the value of x can be evaluated as;
x = 3²⁰/3
x = 3¹⁹.
Ultimately, the value of x from the given equation is; 3¹⁹.
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A teacher runs each morning before school. Last week, he ran a total of 5 3/4 miles. This week, he ran 4/5 of the total number of miles he ran last week. What is the total number of miles that the teacher ran last week and this week?
The total number of miles that the teacher ran both last week and this week was 10.35 miles
How to find the total number of miles?Last week, the teacher ran a total of 5 3/4 miles. For easier calculation, convert this to a decimal:
= 5 + 3/4
= 5 + 3 ÷ 4
= 5 + 0.75
= 5.75 miles
This week, the teacher ran 4 / 5 of the miles he ran the previous week:
= 5. 75 x 4/5
= 4.6 miles
The total number of miles the teacher ran both last week and this week were:
= 5.75 + 4.6
= 10.35 miles
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Answer:
10 7/20 miles
Step-by-step explanation:
Find the average for the set of numbers 7, 6, 12, 5, 7, 6, 13. Average:
Answer:
Add up all the numbers and divide the product of that by the numbers there are.
7+6+12+5+7+6+13 = 56
There are 7 numbers in these set of numbers hence we divide the product (56) by 7.
56/7 = 8
The answer is 8; The average of all these numbers is 8.
Step-by-step explanation:
Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. Their investments are in the ratio
1:2:0.5, respectively.
How much has Zach invested, in dollars?
Enter your answer in the space provided.
Zach's investment is $100,000.
A ratio shows us the number of times a number contains another number.
Given that Zach, Kolby, and Peyton are investing a total of $350,000 to open a coffee shop. And their investments are in the ratio 1:2:0.5, respectively.
Therefore, Zach, Kolby, and Peyton's investment can be written as 1x, 2x, and 0.5x, respectively.
Now, the total sum of the investment of the three can be written as,
Zach's investment + Kolby's investment + Peyton's investment = $350,000
1x + 2x + 0.5x = $350,000
3.5x = $350,000
x = $350,000 / 3.5
x = 100,000
Further, Zach's investment can be written as,
Zach's investment = 1x = 1($100,000) = $100,000
Hence, Zach's investment is $100,000.
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let o be the point of intersection for the diagnols of quadrilateral abcd prove that abcd could be a trapezoid (that is if it has one sides parallel) is Aaod = Aboc
From the given proof below, we have been able to show that quadrilateral ABCD is a Trapezoid.
How to identify a Trapezoid?A trapezoid is also called a trapezium and it is characterized by four straight sides and one set of parallel sides. The parallel sides are referred to as the base, while the non-parallel sides are referred to as the legs.
We are told that;
O is the point of intersection for the diagonals of quadrilateral ABCD;
where;
AO/BO = CO/DO
This can also be expressed as;
AO/CO = BO/DO
Thus, if we create line OE to be parallel to DC which is OE || DC. Then it means that point E lies on BC.
Using the Basic Proportionality Theory, in ΔBDC, we can say that;
BO/OD = BE/EC ............................1
We are also given that:
AO/CO = BO/DO ..........................2
Thus, from Equations 1 and 2, we have;
AO/CO = BE/EC
Using the converse form of the Basic Proportionality Theorem, we have;
OE || AB
Therefore, AB || OE || DC.
Therefore we can conclude that ABCD is a Trapezoid.
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Estimate 17.140 - 03.179 by first rounding each number to the nearest tenth.
Answer: 13.9
Step-by-step explanation:
17.140 rounded to the nearest tenth is 17.1
03.179 rounded to the nearest tenth is 3.2
17.1 - 3.2 = 13.9
a- 10 units
b-12.0 units
c-11.4 units
d-13.4 units
Using the distance formula, the distance between the point is √130.
In the given question we have to find the distance between given point in the graph.
From the graph the given points are (4,4) and (-3, -5).
The formula for the distance between point is
Distance = √{x(2)-x(1)}^2+{y(2)-y(1)}^2
From the given points; x(1)=4, y(1)=4, x(2)= -3 and y(2)= -5.
Now putting the value:
Distance = √{-3-4}^2+{-5-4}^2
Distance = √{-7}^2+{-9}^2
Distance = √49+81
Distance = √130
The distance between the point is √130.
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Elijah has red and yellow napkins. He must set out napkins for 4 people. What are different ways to make groups of 4?
The different ways to make groups of 4 based on the napkins given is 6 ways.
What is combination?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Thus can be illustrated by nCr
Combination formula
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
In this case, Elijah has red and yellow napkins. He must set out napkins for 4 people. This will be:
= n! / ((n – r)! r!)
= 4! / (4 - 2)! 2!
= 4! / 2!2!
= 4 × 3/2
= 6
Therefore, there are 6 ways.
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A laundromat has a wash-and-fold service for a monthly fee of $28.00. The laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service. One customer paid $41.42 in total for the month.
Which equation can be used to determine the pounds of laundry the customer brought in to be washed and folded that month?
A. 0.61x + 28.00 = 41.42
B. 0.61x + 41.42 = 28.00
C. 28.00 - 0.61x = 41.42
D. 41.42 + 28.00 = 0.61x
The required equation can be used to determine the pounds of laundry the customer brought in is A. 0.61x + 28.00 = 41.42
What is an equation?An equation is a mathematical expression that shows the relationship between two variables.
How to find equation can be used to determine the pounds of laundry the customer brought in to be washed and folded that month?To find the given equation,
Let x be the number of pounds of clothes washed and folded at the laundromat.
Given that the laundromat will wash and fold clothes at $0.61 per pound for those customers with a laundry service, the total amount paid for the number of poundsof clothes is P = rate × number of pounds = $0.61 × x = 0.61x
Also, the laundromat has a wash-and-fold service for a monthly fee of $28.00.
So, the total amount paid is T = P + $28.00 = $0.61x + $28.00
Now, since one customer paid $41.42 in total for the month, since this is the total amount paid, then T = $41.42
So, $0.61x + $28.00 = $41.42
So, the required equation is A. 0.61x + 28.00 = 41.42
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Like terms 8x-12-10x-8
Find the ordered pairs corresponding to the x- and y-intercepts of the graph of the equation.
6x + 12y = 24
Answer:
6x=24-12y
x=24-12y/6
x=4-12y
Write a quadratic function f whose zeros are 7 and -5.
Answer:
f(x) = x² -2x -35
Step-by-step explanation:
You want a quadratic function that has zeros 7 and -5.
FactorsEach zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).
f(x) = (x -7)(x +5)
f(x) = x² -2x -35
__
Additional comment
You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.
sum: 7-5 = 2
product: (7)(-5) = -35
quadratic: f(x) = x² -2x -35
adult tickets
A total of 390 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times ti
number of adult tickets sold. How many adult tickets were sold?
The number of adult tickets were sold is 130 tickets.
Given,
In the question:
Total tickets were sold for the school play is 390 tickets.
The number of student tickets sold was two times number of adult tickets sold.
To find the how many adult tickets were sold?
Now, According to the question:
Based on the given conditions:
Let the number of adult tickets be x.
Formulate the condition:
x × (1 + 2) = 390
x × 3 = 390
Simplify
x = 390/3
x = 130
Hence, The number of adult tickets were sold is 130 tickets.
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Which graph represents the function f(x) = –|x + 3|?
Answer:
The answer would be A. (Not sure if its A B C or D question but I will have picture below)
Step-by-step explanation:
Hope this helps you! :))
4x7 = 2x + 15
Does the equation have one
none, or infinite solutions?
Explain why.
Answer:
There is only one solution
Step-by-step explanation:
4x - 7 = 2x + 15
+7 +7
4x = 2x + 22
-2x -2x
2x = 22
divide by 2 into both sides
x = 11
Since there is only one answer, there is only ONE solution.
It takes an older computer 3 times as long to send out a company's email as it does a newer computer. Working together, it takes the two computers 15 minutes to send out the email. How long will it take the older computer to send out the email on its own?
60 minutes will be taken by the older computer to send out the email on its own.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
one computer takes x minutes and the other takes 3x minutes
in 1 minute, they send (1/x) and (1/3x) of the total message
together, (15/x)+(15/3x)=1, the full message
multiply by 3x to clear fractions
45+15=3x
60=3x
Divide both sides by 3
20=x
So for older computer 60 minutes it take to send out the email on its own.
Hence, 60 minutes will be taken by the older computer to send out the email on its own.
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If the quotient is 0 , what is the dividend?
Answer: 0
Step-by-step explanation:
If the dividend and the divisor are the same, the quotient is always 1. If the dividend is the, then the quotient would always be 0. A division equation with 0 dividend and 0 divisor is not valid.
Answer: All real numbers
Step-by-step explanation: Anything that's being divided by 0, is always going to be 0. For example, 0/7 is always 0.
add w and the sum of 9 and 4
The addition of w, 9 and 4 is (w+13).
According to the question,
We have the following information:
We need to add w, 9 and 4.
We already know that a variable can only be added or subtracted from the terms having the same variables. For example, 8x can only be added to 5x but not 5y.
So, in this case, w is the variable and it can not be added to any other term because the other two are whole numbers.
Now, the whole numbers can be easily added.
So, we have the following expression:
w+9+4
w+13
Hence, the addition of w, 9 and 4 is (w+13).
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Luis has $80 in his checking account. He makes a deposit of $100, and the write a check for $40
Answer: 140 is the answer
Step-by-step explanation: Luis adds 100 to his account so which makes the account balance 180 and then writes a check so he takes 40 out of his account which means he has 140 left in his account
need help asap please
Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. Jada gets if she allows s to take on any value between 0 and 7.5.
The domain of the function that represents Jada's trip is the set of input value the function can take
The appropriate domain is all real numbers except
x = 5.5
by looking at the graph, we can see that:
The x-value starts at negative infinity, and ends near 5.5
The x-value then continues near 5.5, and ends at positive infinity
This means that the input of the graph cannot be 5.5
Hence, an appropriate domain would be: x # 5.5
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Find the value of n(AnB) if
n(A)=5 n(B)=7 and n(AUB)= 10
what is n(AnB)=?
PLEASE HELP
By using the concept of set operation, the result obtained is
[tex]n(A \cap B) = 2[/tex]
What is a set?
Set is a well defined collection of distinct objects. The members of a set are called elements of a set. Set can be empty as well as non empty.
Set can be finite as well as infinite.
The number of elements inside a set is known as cardinal number of the set
Operations on set are union, intersection, set difference and symmetric difference
Concept of set operation has been used here
n(A)=5 n(B)=7 and n(AUB)= 10
[tex]n(A \cap B) = n(A) + n(B) - n(A \cup B)[/tex]
[tex]n (A \cap B) = 5 + 7 -10\\n(A \cap B ) =2[/tex]
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PLEASE HELP EXTRA POINTS select all true statements
Answer: C
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form or standard form. Express numbers as integers or
simplified fractions.
The line contains the point (-3, 6) and is parallel to 3x+3y=2.
The equation of the line is
The equation of the line is : y = -1x + 3
What is Equation of line?
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
Given,
3x + 3y = 2
3y = -3x + 2
y = -x + 2/3
Comparing it with
y = mx + c
we get,
m = -1
Now, let the equation of line be
y = mx + c
where, m = -1
Now we have to check for point (0,0) that it satisfies
0 = -1(0) + c
c = 0
So, the equation of line will be y = -1x
Now, let y = mx + c be the equation of line of point (-3, 6) should satisfy]
6 = -1(-3) + c
6 = 3 + c
c = 6 - 3
c = 3
So the equation of line is y = -1x + 3
Hence, The equation of the line is y = -1x + 3
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NO LINKS!! Explain the process of constructing a 95% confidence interval to test a null hypothesis and what a 95% confidence interval represents. (Use either proportions or means).
At 95% confidence, the z critical value is roughly z = 1.96
You would use a reference table or calculator to determine this value. Unfortunately it's not something that can be easily/quickly found by hand.
If we're trying to estimate the population mean (mu), then we'll use this margin of error formula
E = z*sigma/sqrt(n)
Or if we want to estimate the population proportion (p), then we use this formula
E = z*sqrt(phat*(1-phat)/n)
The confidence interval then spans from (pointEstimate)-E to (pointEstimate)+E. Where "pointEstimate" represents either xbar or phat depending on the context. Other point estimates are possible. We're focusing on these two for now.
xbar estimates mu
phat estimates p
--------------------------------
An example problem:
A manager at a soda bottling plant wants to know if the contents of the cans are 20 fluid ounces (fl oz) or not. Through past observations, the manager has noted the population standard deviation (sigma) is 1.72 fl oz.
The manager gathers a random sample of 50 cans to test their contents. They find the sample mean is 18 fl oz. Conduct a hypothesis test using a confidence interval at 95% confidence to see if the cans really do have 20 fl oz of drink in them or not.
--------------------------------
Solution:
Null Hypothesis: mu = 20
Alternate Hypothesis: mu ≠ 20
This is a two-tailed test.
E = margin of error
E = z*sigma/sqrt(n)
E = 1.96*1.72/sqrt(50)
E = 0.47676
L = lower boundary of confidence interval
L = xbar - E
L = 18 - 0.47676
L = 17.52324
L = 17.52
U = upper boundary of confidence interval
U = xbar + E
U = 18 + 0.47676
U = 18.47676
U = 18.48
The 95% confidence interval is approximately (17.52, 18.48)
This is equivalent to writing 17.52 < mu < 18.48 in which we are 95% confidence in saying mu is between those endpoints.
But wait, the hypothesized mu = 20 is not in the interval 17.52 < mu < 18.48, which indicates we must reject the null hypothesis and accept the alternate hypothesis.
The soda cans do not have 20 fl oz of drink. It appears they have slightly less than 20 fl oz.
Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log4 (6(5 + 2x)). Make sure
to use parenthesis around your logarithm functions log(x + y).
[tex]log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)[/tex] is the completely expanded logarithmic expression .
What are logarithms ?Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.
The most common types of logarithms are the base 10 common logarithm, the base 2 binary logarithm, and the base e ≈ 2.71828 natural logarithm.
Calculationsthe product rule for logarithms is
[tex]log_{b}(MN) = log_{b}(M) + log_{b}(N)[/tex] for b > 0
now ,
[tex]log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)[/tex]
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State whether the following variables have a positive correlation, negative correlation, or no correlation.
3.)
(a.)Height of a person and how often he or she attends religious services. __________________________________
(b.)Average property tax in a school district and salary of teachers __________________________
(c.)Weight of a person and shoe size. ____________________________
The types of correlation seen between positive correlation, negative correlation, or no correlation, in the variables is:
a. Height of a person and how often he or she attends religious services. - No correlation (b.)Average property tax in a school district and salary of teachers - Positive correlation (c.)Weight of a person and shoe size. - Positive correlation What is the correlation between property taxes and teacher salaries?One of the main sources of funding for school districts is the property tax charged. This means that increased property taxes will lead to more money being available for teacher salaries which might then increase. There is therefore a positive correlation between the two.
The same is true for the weight of a person and shoe size. This is because the heavier a person is, the larger their shoe size according to research.
There is however no correlation between the height of a person and their attendance of religious services.
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Help pls I need a fraction answer
7 4/10 + 2/10 =
Answer: 7 4/10 + 2/10 = 38/5 = 7 3/5 = 7.6
Answer Overall : 38/5
Step-by-step explanation: Conversion a mixed number 7 4/10 to a improper fraction: 7 4/10 = 7 4/10 = 7 · 10 + 4/10= 70 + 4/10= 74/10
To find a new numerator:
a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10
b) Add the answer from previous step 70 to the numerator 4. New numerator is 70 + 4 = 74
c) Write a previous answer (new numerator 74) over the denominator 10.
Seven and four tenths is seventy-four tenths
Add: 74/10 + 2/10 = 74 + 2/10 = 76/10 = 2 · 38/2 · 5 = 38/5
The common denominator you can calculate as the least common multiple of both denominators - LCM(10, 10) = 10. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 38/5.
In other words - seventy-four tenths plus two tenths is thirty-eight fifths.
First convert the mixed number to a fraction by multiplying 7 by 10 and adding 4
74/10+2/10add them together but DONT add the denominators
76/10These numbers can be simplified by 2 so the final answer is:
38/5Evaluate the expression when x =-4
Answer:
22. 2 (-4) = -8
23. (2(-4) + 11) = (-8 + 11) = 3
24. -3 (5 (-4) = -3 (-20) = 60
Answer:
22. 8
23. 3
24. -60
Step-by-step explanation:
You want the values of the given absolute value expressions when x = -4.
23. 2|x|The absolute value function changes the sign to positive, if it isn't already.
2|-4| = 2(4) = 8
24. |2x +11||2(-4) +11| = |-8 +11| = |3| = 3
25. -3|5x|-3|5(-4)| = -3|-20| = -3(20) = -60
To adopt a dog from an animal shelter, you must pay $80 for vaccinations, $65 to spay or neuter the dog, and $50 for a wellness exam by a veterinarian.
a. Write an expression in the simplest form that represents the amount (in dollars) it costs to adopt x dogs.
An expression is (?) dollars.
Question 2
b. What does the coefficient of the expression in part (a) represent?
Responses
the total cost (in dollars) of adopting one dog
the total cost (in dollars) of adopting one dog
the total amount (in dollars) the veterinarian is paid when one dog is adopted
the total amount, (in dollars), the veterinarian is paid when one dog is adopted
the total cost (in dollars) of adopting x dogs
the total cost (i, n dollars), of adopting x dogs
the total amount (in dollars) the animal shelter earns when x dogs are adopted
the total amount (, in dollars) the animal shelter earns when , x, dogs are adopted
please and thank you!
Answer:$190
Step-by-step explanation:
for an expression is $80+$65+$50=190 per dog to adopt a from the animal shelter.