Answer:
GCF = 6; sum = 6(1 +3)
Step-by-step explanation:
You want the greatest common factor of 6 and 18.
GCFThe greatest common factor is the largest factor common to both numbers. Here, we can factor the numbers as ...
6 = 6·1
18 = 6·3
The factor 6 is common to both numbers. (Other numbers, such as 1, 2, and 3 are also common factors, but 6 is the largest.)
The GCF is 6.
In terms of the GCF, the sum can be written ...
6 +18 = 6(1 +3)
__
Additional comment
If the smaller number is not a factor of the larger, then the next value to check is the difference between the larger and smaller.
Euclid's algorithm tells you the remainder from division of the larger by the smaller will be zero when the divisor is the GCF. Otherwise, the remainder can be used to replace the larger number for trying again.
Here, 18/6 = 3 r 0, so 6 is the GCF.
Forty-five percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 125 randomly selected individuals and found 50 believed that there is life on other planets. At α=0.10, is there sufficient evidence to conclude that the percentage differs from 45%? Use the P-value method with tables.
Hypothesis test is a two-tailed test. Compute the test value. Always round z score values to two decimal places.
We will reject the H0 as there sufficient evidence is obtained that the percentage of people who believe that there is life on planets differs from 50%.
It is given that the sample size, (N) is 125
Probability (P)= 0.50 or 50%
P'= 50/120= 0.4166
Significance level ([tex]\alpha[/tex])=0.10
If we consider the null and alternative hypotheses, they are:
H0= 0.50
H1≠ 0.50
For conducting the test statistics:
Z= [tex](P'-P)/\sqrt{P*(1-P)/N}[/tex]
Z= [tex](0.41-0.50)/\sqrt{0.50*0.50/125}[/tex]
Z= -2.01
The critical value of Z at [tex]\alpha[/tex]=0.10 is 1.645 or -1.645
And the P- value at Z= 2.01 is 0.04
Decision Criteria: If the P-value is less than the significance level, we reject the H0. Also, if the Z is found to be greater than the critical value, we will reject H0.
Thus, in this case, we see that, the P-value, 0.04 is less than the significance level, i.e., 0.10, we will reject the H0.
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A pentagon is made up of an equilateral △ABC of side length 2cm on top of a square BCDE. Circumscribe a circle through points, A,D and E. The radius of the circle isA1+√32B5−2√3C 2D 1+√3
An equilateral △ABC with a side length of 2 cm is placed on top of a square BCDE to form a pentagon. A circle is drawn including points A, D, and E. And the radius of this circle is found to be 2 cm.
A triangle is said to be equilateral if all three of its sides are the same length and each of its three angles measures 60 degrees.
The given triangle is equilateral with a side length of 2cm. This triangle is on the top of a square BCDE. The circle circumscribes through the A, D, and E of the given shapes.
Using the given details, first, draw the diagram. Let H is the circumcenter of ADE. In the diagram, draw the altitude of AG passing through the circumcenter and square as GF.
From the diagram, let GH be x. The side of the triangle is 2 cm and the altitude cut it into two equal halves. Then, BG=EF=1 cm, HF=2-x, and HE=x+√3
[tex]\begin{aligned}\sin \theta &= \frac{AG}{AB}\\\sin 60^{\textdegree} &=\frac{AG}{2}\\\frac{\sqrt{3}}{2}&=\frac{AG}{2}\\AG&=\sqrt{3}\end{aligned}[/tex]
By Pythagoras' theorem, from ΔHEF,
[tex]\begin{aligned}HE^{2}&=HF^{2}+EF^{2}\\\left(x+\sqrt{3}\right)^2&=(2-x)^2+1^2\\x^2+3+2\sqrt{3}x&=4-4x+x^2+1\\(4+2\sqrt{3})x&=5-2\\x&=\frac{2}{4+2\sqrt{3}}\\&=\frac{2}{2(2+\sqrt{3})}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\\&=\frac{2-\sqrt{3}}{4-3}\\&=2-\sqrt{3}\end{alinged}[/tex]
The radius of the circle (HE) is 2-√3+√3=2.
The answer is 2 cm. Therefore, option C is correct.
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The mean number of hours watching TV per week for a sample of 153 teenagers is 27. If the margin of error for the population mean with a 98% confidence interval is 1.2, construct a 98% confidence interval for the mean number of hours watching TV per week for all teenagers.
With 98% confidence interval, all teenagers' mean number of hours watching TV per week will be (26.6,29.4).
98% confidence interval can be calculated as
Point estimate± Error margin
Point estimate=mean number of hours watching TV
students=28.
Error margin=1.4.
As per given data, the 98% confidence interval for all teenagers is
=28± 1.4
=(28-1.4,28+1.4)
=(26.6,29.4)
Statisticians use confidence intervals to assess the level of uncertainty in a sample variable. For instance, a researcher may select numerous samples at random from the same population and compute a confidence interval for each sample to estimate how each sample may correctly reflect the true value of the population variable. With certain intervals including the true population parameter and others not, each produced dataset is distinct. Confidence intervals are a set of values that are constrained by the mean of the statistic and are likely to include an unidentified population parameter. The confidence level is the proportion of likelihood, or certainty, that, after multiple draws from a random sample, the confidence interval would contain the true population parameter.
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x:2 + 8 =-24[tex]x/2 + 8 =-24.which step should sammy complete first
The step which Sammy should complete first in a bid to solve the equation is; subtraction 8 from both sides of the equation.
Which step should Sammy complete first to solve the equation?It follows from the task content that the step which Sammy should complete first in a bid to solve the equation.
Since the given equation is;
x/2 + 8 = -24
Therefore, in a bid to solve the equation; the first step which Sammy must complete first in a bid to solve the equation is;
Subtract 8 from both sides of the equation; so that we have;
x/2 = -24 -8
x/2 = -32
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What percent of 60 is 51?
Answer:
85%
Step-by-step explanation:
Hope it helps!
Answer:
85%
Step-by-step explanation:
51/60=.85=85%
of the 459,000 people living in miami, 68%indicated on a recent, city-wide survey that they were employed for a random sample of size 490 people, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?
The standard deviation of the sampling distribution of sample proportions is 0.21
Given,
Number of people living in Miami = 459,000
Sample size, n = 490 people
Population proportion, p = 68% = 68
We have to find the standard deviation for the sampling distribution of the sample proportions;
Here,
Standard deviation of the sampling distribution of sample proportions is
σpˆ=√p(1−p)/n
σpˆ=√.68(1-.68)/490
σpˆ= .021
That is,
0.21 is the standard deviation of the sampling distribution of sample proportions.
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rewrite x+6=0 in slope intercept form
Answer:x=6
Step-by-step explanation:You can simplify as 0 is worh nothing so it would be just 6
HELP
Select all the equivalent solution sets to the compound inequality 27>−1/2(4x+6)≥100?
A. −15
B. −10.5
C. −10.5
D. −15
E. −10.5
F. −15
G. −15
The ______________ function is used to compute the number of times a particular condition is satisfied within a given range of cells.
The COUNTIF function is used to compute the number of times a particular condition is satisfied within a given range of cells.
What is countif?It is an excel statistical function, which is used to count the number of cells that meet a criterion. To determine how many cells in the worksheet contain a number higher than or less than the one specified, the countif formula is used.
It is typed =COUNTIF
Steps to use the =COUNTIF function:1. Select a cell
2. Type =COUNTIF
3. Double-click the COUNTIF command
4. Select a range
5. Type
,6. Select a cell (the criteria, the value that you want to count)7.
Hit enter Hence the answer is COUNTIF
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Mary has 7 1/12 square feet of wrapping
paper. If she needs 1 3/5 times more paper
than what she has, how many more feet of paper does she need?
Answer: 12
Step-by-step explanation:
Convert both mixed numbers to improper fractions:
7 1/12= 85/12
1 3/5= 8/5
Multiply:
84 x 8 = 680
12 x 5 = 60
As a fraction:
680/60
Simplified:
11 1/3 ft. of paper needed
(c) a farm brings 11 tons of watermelon to market. find a 92% confidence interval for the population mean cash value of this crop. what is the margin of error? hint: 1 ton is 2000 pounds. (round your answers to the nearest dollar.)
The farm's 11 tons of watermelon will have a 92% confidence interval mean cash value of $148.89, which is within the margin of error.
What is margin of error?In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and study results using the margin of error. Your findings will vary from the actual population figure by how many percentage points, as shown by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.
Here,
n = 38
x = 6.88
= 1.86
= 1-.90
= .10
/2 = .05
z(/2) = -1.64
-z(/2) = 1.64
P(-1.645 < z < 1.645) = .90
Margin of error= z(/2)(/√n)
= 1.645(1.86/√38)
= $.4963(300)
= $148.89
The margin of error for a farm brings 11 tons of watermelon to market with 92% confidence interval for the population mean cash value of this crop will be $148.89.
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What is 1\3x + y = 4
a four digit personal identification number (pin) is selected. what is the probability that there are no repeated digits? do not round
If a four digit personal identification number is selected, then the probability that there are no repeated digits is 0.504
Number of digits in the identification number = 4
0, 1, 2, 3, 4, 5, 6, 7, 8 and 9
There are 10 digits
The probability = Number of favorable outcomes / Total number of outcomes
Total number of outcomes = 10 × 10 × 10 × 10
= 10000
Number of outcomes that digits wont repeat = 10 × 9 × 8 × 7
= 5040
Substitute the values in the equation of probability
The probability = 5040 / 10000
= 0.504
Therefore, the probability there are no repeated digits is 0.504
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g consider a disk queue holding requests to the following cylinders in the listed order: 94, 169, 39, 135, 22, 133, 69, 65. using each of the following scheduling algorithms, what is the order in which the requests will be serviced? (assume that the disk head is currently located at cylinder 50 and is moving toward higher numbered cylinders).
For FCFS (First Come, First Served):The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65.
SSTF (Shortest Seek Time First):
The requests will be serviced in the following order: 39, 22, 65, 69, 94, 133, 135, 169
SCAN:
The requests will be serviced in the following order: 39, 65, 69, 94, 133, 135, 169, 22
C-SCAN:
The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65
LOOK:
The requests will be serviced in the following order: 39, 65, 69, 94, 133, 135, 169, 22
C-LOOK:
The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65
In FCFS and C-SCAN, the requests are serviced in the same order as they were received. In SSTF and LOOK, the requests are serviced in an order that minimizes the seek time of the disk head. In SCAN and C-LOOK, the requests are serviced in an order that moves the disk head in one direction (towards higher numbered cylinders in this case) until the end of the disk is reached, and then moves the disk head in the opposite direction to service the remaining requests.
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a variable is normally distributed with mean 19 and standard deviation 5. use your graphing calculator to find each of the following areas. write your answers in decimal form. round to the nearest thousandth as needed. a) find the area to the left of 16. b) find the area to the left of 14. c) find the area to the right of 15. d) find the area to the right of 27. e) find the area between 14 and 30.
The areas are
(a) 0.2743
(b) 0.1587
(c) 0.8413
(d) 0.0548
(e) 0.8274
What is standard deviation ?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
Use TI 84 plus calculator to find the following areas
(a) Entering the values
Lower : -999999999
Upper : 16
Area (probability): 0.2743
(b) Entering the values
Lower : -999999999
Upper : 14
Area (probability): 0.1587
(c) Entering the values
Lower : 15
Upper : 999999999
Area (probability): 0.8413
(d) Entering the values
Lower : 27
Upper : 999999999
Area (probability): 0.0548
(e) Entering the values
Lower : 14
Upper : 30
Area (probability): 0.8274
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A shipping container will be used to transport several 60 kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 24500 kilograms. Other shipments weighing 14600 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine x, the number of 60 kilogram crates that can be loaded into the shipping container.
The inequality which can be used to determine x, the number of 60 kilogram crates that can be loaded into the shipping container is
60x ≤ 9900 where x is less than or equal to 165
What is an Inequality?
Inequalities are the mathematical expressions in which both sides are not equal.
In inequality, unlike in equations, we compare two values.
The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
According to the given question:
The greatest weight that can be loaded into the container is 24500 kilograms.
Other shipments weighing 14600 kilograms have already been loaded into the container.
24500 - 14600 = 9900 kg can be the weight of 60 kg containers
Now, the number of 60 kilogram crates that can be loaded into the shipping container can be represented as
60x ≤ 9900
where x is number of 60 kg containers
Solving for x we get
x ≤ 165
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if a true-false test with questions is given, what is the probability of scoring (a) exactly 80% just by guessing?
The probability of scoring exactly 80% is 0.04395 as per the given data.
Given: 10 true-false questions
So, we will have 50% chances (probability = 0.5) of being correct.
P( 80% score) = P( 8 answers correct)
As we observe, if X= number of correct answers, then X~ Binomial (n=10, p=0.5)
So, P( 80% score) = P( 8 answers correct)
= 0.0439453125
= 0.04395
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
Probability basically refers to the degree to which something is likely to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will discover the possible results for a random experiment. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
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how many three-digit numbers can be formed using the digits 1 through 9 if no digit can appear twice in a number?
Total 504 three digit numbers can be formed if no digit appear twice
What is Permutation?
The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.
Solution:
Total Numer of Digits = 9
Number of Characters in the number = 3
Total Numbers = 9P3 = 9! / 6!
9P3 = 504
Total 504 three digit numbers can be formed
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If you bought a stock last year for a price of $79, and it has gone down 8.7% since then, how much is the stock worth now, to the nearest cent?
Answer:
72.13
Step-by-step explanation:
If you bought a stock last year for a price of $79, and it has gone down 8.7% since then, how much is the stock worth now, to the nearest cent?
Helpppppppppp meeeeee
Answer:
1.07 maybe... don't trust me on that
Answer:
x = -6
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.
We can write the following equation based on this information to calculate value of x:
64 + 27 = 97 + x
Add like terms91 = 97 + x
subtract 97 from both sides91 - 97 = 97 - 97 + x
-97 will eliminate the 97 on the right side of the equation-6 = x
Subtract and choose the answer in simplest form.
1\frac {(3)} {(4)}-\frac {1} {3}
(4)
(3)
−
3
1
The required evaluation to the given expression is 5/12.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The expression is given in the question as:
1 3/4 - 1/3 (4)(3) - 1/3
We have to determine the evaluation to the given expression
As per the given question, we have
⇒ 1 3/4 - 1/3 (4)(3) - 1/3
⇒ 7/4 - 1/3 (12) - 1/3
Apply the subtraction operation,
⇒ 7/4 - 4 - 1/3
Take the LCM in the above fractions,
⇒ (21 - 12 - 4)/12
⇒ 5/12
Thus, the required evaluation to the given expression is 5/12.
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a cake recipe calls for 472 ml of milk. you dont have a metric measuring cup at home, so you need to convert milliliters to cups. you know that 1 l equals 1.06 quarts and that there are 4 cups in 1 quart. how many cups of milk will you need to use
Number of cups of milk that will you need to use is 2.001 cups
Total quantity of milk needed for the cake = 472 milliliter
we know
1 liter = 1.06 quarts
1 quart = 4 cups
Convert the given quarts to cups
Then 1.06 quarts = 4 × 1.06
Multiply the numbers
= 4.24 cup
Here the total quantity of milk needed for the cake is 472 milliliter
We have to use the unitary method here
1 liter = 4.24 cups
472 milliliter = 4.24 × 0.472
Multiply the numbers
= 2.001 cups
Therefore, he need 2.001 cups of milk to make a cake
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A gas station is open 365 day a year, 24 hours a day. The store owner estimates that they served 40,000 cups of coffee last year. This quantity can also be expressed as
functions
equation editor
cups of coffee per hour (round to the nearest whole cup). This is a ? reasonable not reasonable estimate.
A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.
The problem can be solved using the average value approach.
Average value = total amount or sum of data / number of data
In the given problem,
total amount = total coffee served last year
total amount = 40,000
number of data = number of hours in a year
number of data = 365 day/year x 24 hours/day = 8760 hours
Hence,
Average value = total amount or sum of data / number of data
= 40000 / 8760
= 4,6 ≈ 5 (round to the nearest whole cup)
Hence, the average coffee served is 5 cups per hour.
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when transforming a shape twice, do you transform it from the pre image or image?
a child has a box full of colored building blocks. he will choose one block without looking. the odds against choosing a blue block are 47. what is the probability of choosing a blue block?
7/11 is the probability of choosing a blue block.
Given:
a child has a box full of colored building blocks. he will choose one block without looking.
the odds against choosing a blue block are 47.
We need the probability of choosing a blue block,
Odds:
The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.
The odds against choosing a blue block are 4/7 means. In 11 chances, 4 events will happen in which blue block will not be chosen and 7 events will happen in which blue blocks will be chosen.
So, the probability of not choosing the blue block is 4/11.
Probability of choosing blue block: complement of 4/11 which is equal to 7/11.
Hence we get the required answer.
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PLEASE HELP 5 QUESTIONS PLEASE ILL GIVE BRAINLY IF IT SHOWS
1.
Which one is a proportion?
A. 1/2 = 2/3
B. 3/4 = 12/16
C. 19/15 = 54/85
D.2.5/7=5/12
-------------------
2.
Solve the proportion for the missing value of y.
3/12 = y/8
y =_________|
----------------------
3.
Solve the proportion for the missing value of w.
5/w = 8/4
w =__________|
-------------------------------
4.
If Mr. Argo went 20 miles on 2.5 gallons of gas, and he wants to know how far he can go on 9 gallons of gas. Which proportion would be helpful to solve the problem?
A.20/9 = 2.5/x
B. 9/2 = 20/x
C. 20/2.5 = x/9
D.9/20 = x/2
Answer:
3/4 = 12/16, y = 2, w = 2.5, 20/2.5 = x/9
Step-by-step explanation:
The first question is asking which is proportional.
B. 3/4 = 12/16
We know this is proportional because 4 can be multiplied by 4 to get 16, and the same can be applied to 3 to get 12.
The second question is asking for the missing value of y.
3/12 = y/8
y = 2
We can solve this by looking at the 12 and the 8.
8 is 2/3 of 12.
2/3 of 3 is 2
The third question is asking for the missing value of w.
5/w = 8/4
w = 2.5
We can solve this by looking at the 8/4.
8/4 is the same as 2/1.
Using this, we can conclude that w = 2.5
The fourth question is asking for the correct proportion.
If Mr. Argo can go 20 miles on 2.5 gallons of gas:
20/2.5
And he wants to know how many miles he can go with 9 gallons:
x/9
We can use the equation: C. 20/2.5 = x/9
Hope this helps!!
identify the expression as a numerical expression or a variable expression. for a variable expression, name the variable. 9 10 variable expression; j is the variable. variable expression; i is the variable. variable expression; there is no variable. numerical expression
As there is no variables, so the given expression 9 + 10 is the numerical expression.
What is numbers ?An object can be counted, measured, or labelled using a number, which is a mathematical value. Arithmetic calculations are often done with numbers. Natural numbers, whole numbers, rational and irrational numbers, among other types of numbers, are examples. A null value is also represented by the integer zero, or 0.
What is numerical expression ?Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.
Mathematical operations like add, subtract, multiply, and divide can be used to mix integers with numbers to create a numerical expression.
Given Expression 9 + 10
As it contains only numbers and mathematical operators,
So, it is the numerical expression.
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chegg the number of successes and the sample size for a simple random sample from a population are given below. x, n, : p, : p, a. determine the sample proportion. b. decide whether using the one-proportion z-test is appropriate. c. if appropriate, use the one-proportion z-test to perform the specified hypothesis test.
Since, it is observed that z = -2.74 < [tex]Z_{\alpha} = -2.33[/tex], it is then concluded that the null hypothesis is rejected.
What is a left-tailed test?
When the alternative hypothesis asserts that the true value of the parameter indicated in the null hypothesis is lower than the null hypothesis indicates, a left-tailed test is utilized.
This is a left-tailed test.
Test statistics
[tex]z = (\hat p - p_{0} ) / \sqrt{} p_{0}*(1-p_{0}) / n[/tex]
= [tex]\sqrt{} (0.4*0.6) / 45[/tex][tex]= ( 0.2 - 0.4) \div \sqrt{} (0.4*0.6) / 45[/tex]
= -2.74
The critical value of the significance level is α = 0.01, and the critical value for a left-tailed test is:
[tex]Z_{\alpha} = -2.33[/tex]
Hence, it is observed that z = -2.74 < [tex]Z_{\alpha} = -2.33[/tex], it is then concluded that the null hypothesis is rejected.
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Anyone willing to help
Answer:
x3=5x+e3x+2−17
This is the best I can do :D
Which of the following has the same value as -5 - 15?
A -15 - (-5)
B-5 + 15
C-5 + (-15)
D-15 + 5
Answer:
C -5 + (-15)
Step-by-step explanation:
-5 - 15 = -20
A -15 - (-5) = -15 + 5 = -10
B -5 + 15 = 10
C -5 + (-15) = -20
D -15 + 5 = -10
Answer:
c; -5+(-15)
Step-by-step explanation:
-5-15=-20
adding a negative number is subtraction, which means;
-5+(-15)=-20
therefore
-5-15=-20=-5+(-15)