The correct way to rewrite the expression 5a + 5b + 5c + 5d using the distributive property is option C) 5(a + b + c + d).
The expression given is 5a + 5b + 5c + 5d. This is a sum where each term is multiplied by 5. According to the distributive property, also known as the distributive law of multiplication, a common factor can be factored out of a sum. The distributive property is represented as (A + B)C = AC + BC. In this case, the common factor is 5, and the sum of the variables a, b, c, and d is grouped, giving us 5(a + b + c + d).
So, the correct representation of the expression is 5(a + b + c + d), which corresponds to option C).
Swati is substituting t=5 and t=9 to determine if the two expressions are equivalent.
Answer:
No the two expressions are not equivalent.
Step-by-step explanation:
the given two expressions t=5 and t=9 are not equivalent because t being a variable cant take two numbers at a same time.however if they are placed in given two expressions of 't' such that that they give equal value when the first expression gives a value 'a' at t=5 while the other expression gives a value 'a' at t=9 then those two expressions will be equal.
Answer:
your answer is D.)
Step-by-step explanation:
20% of the tickets sold at a water park were adult tickets. If the park sold 55 tickets in all,how many did it sell?
Answer:
11 adult tickets
Step-by-step explanation:
I guess you want the number of adult tickets sold.
That is 20% of 55
= 0.20*55
= 11 (answer)
Answer:
the answer is 11
Step-by-step explanation:
I did the math its 11
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Simplify the expression.
Answer:
a. x-3/x+2
Step-by-step explanation:
Answer: A
Step-by-step explanation:
[tex]\dfrac{x^{2}+x-6}{x^{2}-4}*\dfrac{x^{2}-9}{x^{2}+6x+9}[/tex]
[tex]=\dfrac{(x+3)(x-2)}{(x+2)(x-2)}*\dfrac{(x-3)(x+3)}{(x+3)(x+3)}[/tex]
[tex]=\dfrac{(x+3)}{(x+2)}*\dfrac{(x-3)}{(x+3)}[/tex]
[tex]=\dfrac{(x+3)(x-3)}{(x+3)(x+2)}[/tex]
[tex]=\dfrac{(x-3)}{(x+2)}[/tex]
Elizabeth and connie are in charge of balloons. They have 27 blue balloons and 63 yellow balloons. What is the greatest number of groups they can put together and use all the balloons
9 groups because thats the greatest common denominator
Find functions f and g so that h(x) = (f ∘ g)(x). h(x) = (6x - 14)8
[tex]h(x)=(6x-14)^8=[g(x)]^8\\\\f(x)=x^8\\\\g(x)=6x-14\\\\(f\ \circ\ g)(x)=(6x-14)^8[/tex]
Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.
Answer:
D. y-intercept = 5
Step-by-step explanation:
I majored in Mathematics
A car salesman had $65100 in total monthly sales last month. He made $1953 in commission from those sales. What is the salesmans commission as a percent of his total monthly sales?
Answer:
3%
Step-by-step explanation:
In order to find out the percent in commissions a car salesman received, you need to divide $1953 by $65100. The result is .03, which translates to 3%.
Hope that helps!
What is 19.51 ÷ 2? And also explain how you found the answer please. Thank YOU!
Answer:
9.755Step-by-step explanation:
From a calculator your answer in the picture.
0.001y^12,
0.008b^6,
-8/27a^15
Written as a cube of a monomial.
[tex]0.001y^{12}=(0.1)^3y^{4\cdot3}=(0.1)^3(y^4)^3=(0.1y^4)^3\\\\0.008b^6=(0.2)^3b^{2\cdot3}=(0.2)^3(b^2)^3=(0.2b^2)^3\\\\-\dfrac{2}{27}a^{15}=\left(-\dfrac{2}{3}\right)^3a^{5\cdot3}=\left(-\dfrac{2}{3}\right)^3(a^5)^3=\left(-\dfrac{2}{3}a^5\right)^3\\\\\text{Used:}\\\\(a^n)^m=a^{n\cdot m}\\\\(ab)^n=a^nb^n[/tex]
The expressions 0.001y^12, 0.008b^6 and -8/27a^15 can be written as the cubes of the monomials 0.1y^4, 0.2b^2 and -2/3a^5 respectively.
Explanation:The expressions provided can be written as a cube of a monomial. A monomial is a single term, and the cube of a monomial is a term raised to the third power. First, let's begin by expressing the coefficients as cubes:
0.001 = (0.1)^30.008 = (0.2)^3-8/27 = (-2/3)^3Then, for the variables, divide the exponent by 3:
y^12 = y^4^3b^6 = b^2^3a^15 = a^5^3Combining the cubed coefficient and the cubed variable, we have:
0.001y^12 can be expressed as (0.1y^4)^30.008b^6 can be expressed as (0.2b^2)^3-8/27a^15 can be expressed as (-2/3a^5)^3Learn more about Cube of a Monomial here:https://brainly.com/question/29612309
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At the art fair, 95 artists exhibited their work. Of those 95 artists, 25 showed sculptures and 48 showed paintings. If 12 showed both scuptures and paintings, how many artists showed only sculptures or paintings?
The anwser is 73
95 artists 25 showed sculptures+ 48 that show paintings= 73 artists showed sculptures or paintings
Final answer:
By using the principle of inclusion-exclusion, we find that 61 artists showed only sculptures or paintings at the art fair.
Explanation:
To find out how many artists showed only sculptures or paintings, we use the principle of inclusion-exclusion in set theory. We start by adding the number of artists that showed sculptures and those that showed paintings:
Artists with sculptures + Artists with paintings = 25 + 48 = 73.
However, since some artists showed both, we must subtract the number of artists who showed both sculptures and paintings to avoid double-counting:
Artists who showed both = 12.
Now, we subtract this number from our previous total:
73 - 12 = 61 artists who showed only sculptures or paintings.
Jim reads 3 newspaper articles every day, and Jessica reads 5 times more than Jim does. How many newspaper articles does Jessica read every day?
Answer:
Jessica reads 15 newspaper articles
Step-by-step explanation:
Jim reads 3
Jessica read 5 times MORE than Jim
5 x 3= 15
So Jessica reads 15 articles
Given segment de is parallel to segment bc, what postulate or theorem can be used to prove the triangles are similar
Which equation has exactly two real and two non real solutions?
Answer:
The first option [tex]x^4-21x^2-100=0[/tex].
Step-by-step explanation:
To have exactly 2 real and two non real solutions, the degree of the polynomial must be a degree 4. Degree is the highest exponent value in the polynomial and is also the number of solutions to the polynomial. This polynomial ha 2 real+2 non real= 4 solutions and must be [tex]x^4[/tex]. This eliminates the bottom two solutions.
In order to have two real and two non real solutions, the polynomial must factor. If it factors all the way like
[tex]x^4-100x^2=0\\x^2(x^2-100)=0\\x^2(x-10)(x+10)=0\\\\x^2=0\\x-10=0\\x+10=0[/tex]
This means x=0, 10, -10 are real solutions to the polynomial. It has no non real solutions. This eliminates this answer choice.
Only answer choice 1 meets the requirement.
Answer:
A. x^4 - 21x^2 - 100 = 0
Thanks in advance for your help, the question is;
Half the first, plus twice the second of two consecutive integers equals 22. What are the two integerrs?
Answer:
8, 9
Step-by-step explanation:
1/2x + 2(x + 1) = 22
1/2x + 2x + 2 = 22
1/2x + 2x = 20
5/2x = 20
5x = 40
x = 8
8, 9
4 + 18 = 22
Answer:
8 and 9
Step-by-step explanation:
hope this helps!
What type of triangle has its circumcenter, its incenter, its centroid, and its orthocenter all at the same point?
The only triangle with the usual triangle centers coincident is an equilateral triangle.
The centroid is the meet of the medians, which are the segments from a vertex to the midpoint of its opposite side. The centroid is the balance point of the triangle. It always divides the medians into a 2:1 ratio, the long piece connected to the vertex.
The circumcenter is the center of the circumcircle, which is the circle through the vertices. That's only going to be the centroid when that 2 part of the 2:1 ratio is the same for each median. That's only going to happen when the sides are the same length so the centroid makes congruent triangles.
The incenter is the center of the inscribed circle, which is the meet of the angle bisectors of each vertex. Again it wont be the centroid unless the sides are equal.
The orthocenter is the meet of the altitudes and it's the same story.
An equilateral triangle is the only type of triangle where its circumcenter, incenter, centroid, and orthocenter coincide at the same point. This unique property emphasizes the symmetry of the equilateral triangle.
Explanation:The type of triangle where its circumcenter, incenter, centroid, and orthocenter are all at the same point is an equilateral triangle. In an equilateral triangle, all sides are equal in length, and all angles are equal to 60 degrees.
An equilateral triangle has the unique property that its circumcenter (intersection of perpendicular bisectors of sides), its incenter (intersection of angle bisectors), its centroid (intersection of medians), and its orthocenter (intersection of altitudes) all coincide at the same point, which is the geometric center and also the triangle's center of mass.
This property is exclusive to equilateral triangles and emphasizes their symmetry. This also applies in three-dimensional forms such as in an icosahedron where each face is an equilateral triangle, demonstrating further the symmetrical properties of these shapes.
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A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
Let c represent the number of children.
Which expression represents the number of parents?
A.) 9−c
B.) c−9
C.) c + 9
D.) c⋅9
The answer of this one is 9-c
G.O. Is going on a hike in the mountains on a hot summer day. He has 4/5 gallon of water that he spilt into 4 bottles. What fraction of a gallon is in each bottle?
Question
G.O. Is going on a hike in the mountains on a hot summer day. He has 4/5 gallon of water that he spilt into 4 bottles. What fraction of a gallon is in each bottle?:
Answer:
i willll GIVE A BRAN....
Your class hopes to collect at least 400 cans of food for the annual food drive. There were 124 cans donated the first week and 121 more the second week. Write an inequality that describes this situation. Let represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. How many cans are needed to meet or surpass your goal?
a. 124 + 121 + > 400; > 155
b. 124 + 121 + 400 ≥ ; ≥ 645
c. 124 + 121 + ≥ 400; ≥ 155
d. 124 + 121 + ≥ 400; ≥ 645 show your work
i will mark a brain.....
Answer: Choice C
The first inequality is [tex]124+121+x \ge 400[/tex]
The second inequality is [tex]x \ge 155[/tex]
Replace x with whatever letter your teacher is using
=========================================================
Let x be the number of cans collected on week 3
Add this to the previous totals (for weeks 1 and 2) to get 124 + 121 + x. I'm going to leave this as is and not simplify. This is so the answer matches up. This total must be greater than or equal to 400, meaning 124+121+x can be 400 or larger.
124+121+x >= 400
245+x >= 400 .... combine like terms
x >= 400-245 .... subtract 245 from both sides
x >= 155
So you need to collect at least 155 cans for the third week so that you'll have at least 400 cans total.
What is the third quartile of this data set 20,21,24,25,28,29,35,37,42
The third quartile value for the given data 20,21,24,25,28,29,35,37,42 is 36.
What is the median of a data set?
The median is the middle value of a data which is arranged in either ascending/descending order.
What is first quartile of a data set?The lower/first quartile is the median of the bottom half of the data.
What is third quartile of a data set?The higher/third quartile is the median of the upper half of the data.
Arranging the given sequence in ascending order:
20,21,24,25,28,29,35,37,42
Calculating the median of this sequence:
Median(odd no. of terms) = ((n+1)/2)th term
Median(9 terms) = ((9+1)/2)th term
Median = 5th term
Median = 28
Now, the upper half of the data is:
29,35,37,42
Median(even no. of terms) = Median of the two middle terms
Median = ((35+37)/2)
Median = 36
Hence the third quartile of the given data is 36
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On the first play of the game, the Wildcats gained 8 yd. What integer represents a gain of 8 yd? Enter your answer in the box.
Answer:
+8
Step-by-step explanation:
They gained 8 yards so it is +8.
Answer: + 8
Step-by-step explanation: A gain is considered a good thing. It is represented with a positive integer. Here, the gain is represented by +8, or simply 8.
(-2/3, (sqrt)5/3) is a point on the unit circle. Find the cosecant of the angle.
Look at the picture.
[tex]\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}[/tex]
We have the right triangle x, y and r. From the Pythagorean theorem we have:
[tex]r^2=x^2+y^2\to r=\sqrt{x^2+y^2}[/tex]
We have the point
[tex]\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)[/tex]
Substitute:
[tex]r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1[/tex]
[tex]\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}[/tex]
Final answer:
The cosecant of the angle can be determined as the reciprocal of the sine value of the angle, which is √3/√5.
Explanation:
Calculating the cosecant of the angle:
To find the cosecant of the angle, we need to use the definition of cosecant which is the reciprocal of the sine function. Since the point (-2/3, √5/3) lies on the unit circle, the y-coordinate (√5/3) can be used as the sine value of the angle.
Therefore, the cosecant of the angle is the reciprocal of the sine value, which is 1/(√5/3) = √3/√5.
The nicotine content in cigarettes of a certain brand is normally distributed with mean
(in milligrams) m and standard deviation s = 0.1. The brand advertises that the mean
nicotine content of their cigarettes is 1.5, but measurements on a random sample of 400
cigarettes of this brand gave a mean of x = 1.52. Is this evidence that the mean nicotine
content is actually higher than advertised? To answer this, test the hypotheses
H0: m = 1.5, Ha: m > 1.5
at significance level a = 0.01. You conclude
A) that H0 should be rejected.
B) that H0 should not be rejected.
C) that Ha should be rejected.
D) that there is a 5% chance that the null hypothesis is true.
Through hypothesis testing, we cannot reject the null hypothesis at the 1% level of significance. Thus, there is no strong evidence to suggest that the mean nicotine content is greater than what is advertised.
Explanation:The subject here is statistics, specifically hypothesis testing. For this problem, we are asked to test the null hypothesis H0: m = 1.5 against the alternative hypothesis Ha: m > 1.5 at 1% level of significance.
Using the given data, we calculate the test statistic (z) using the formula: z = (x - µ) / (s/√n), where x is the sample mean, µ is the population mean, s is the standard deviation, and n is the sample size. Substituting the given values, we get z = (1.52 - 1.5) / (0.1/√400) = 2.
The z-score at 0.01 level of significance is -2.33 on the left and 2.33 on the right. As our test statistic (2) falls within this range, we fail to reject the null hypothesis (H0: m = 1.5). This suggests that there's no strong evidence to support that the mean nicotine content is greater than advertised.
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Caitlan went to the store to buyschool clothes . She has store credit from a previous return in the amount 39.58. If she bought 4 of the same style shirt in different colors and spent total of 52.22 after the store credit was taken off he total, what was the price of each shirt ahe bought? Write and solve and equation with integrr coefficients
Answer:
each shirt costs $22.95
Step-by-step explanation:
39.58 + 52.22 = 91.80
91.80/4= 22.95
To find the price of each shirt Caitlan bought, use an equation to solve for the cost per shirt, which is $3.16.
Equation: Let x be the price of each shirt. Caitlan spent $52.22 on 4 shirts, so 4x = $52.22. After deducting the store credit, her total spending was $52.22 - $39.58 = $12.64. Therefore, 4x = $12.64. Now, solve for x:
4x = $12.64
x = $12.64 / 4
x = $3.16
Therefore, the price of each shirt Caitlan bought was $3.16.
A local bake shop sells cookies and cakes.On monday , sean bought 3 cookies and 5 cakes and spent $78.75 on tuesday , sean bought 8 cookies and 2 cakes and spent $40 . Find the price of one cookie and one cake .
Answer:
The price of one cookie is $1.25 and the price of one cake is $15.
Step-by-step explanation:
Let $x be the price of one cookie and $y be the price of one cake.
1. On Monday, Sean bought 3 cookies and 5 cakes, then he spent $(3x+5y) and this is $78.75. Thus,
[tex]3x+5y=78.75.[/tex]
2. On Tuesday, Sean bought 8 cookies and 2 cakes, then he spent $(8x+2y) and this is $40. Thus,
[tex]8x+2y=40.[/tex]
3. Solve the system of two equations:
[tex]\left\{\begin{array}{l}3x+5y=78.75\\8x+2y=40\end{array}\right.[/tex]
Multiply the first equation by 2 and the second equation by 5 and subtract them:
[tex]2(3x+5y)-5(8x+2y)=2\cdot 78.75-5\cdot 40,\\ \\6x+10y-40x-10y=157.5-200,\\ \\-34x=-42.5,\\ \\x=\$1.25.[/tex]
Then
[tex]8\cdot 1.25+2y=40,\\ \\2y=40-10,\\ \\y=\$15.[/tex]
Use the substitution method to solve the system of equations
Answer:
(2,4)
Step-by-step explanation:
Take the 2x from y=2x and plug it into the y for 3x+y=10
You now have 3x+2x=10
Combine like terms so 5x=10 then divide by 5x to both sides and x=2
Then plug in 2 for x in y=2x so it becomes y=2(2) y=4
So the answer is (2,4)
The following is an illustration of a regular polygon:
Answer:
False
Step-by-step explanation:
A regular sided polygon means all the sides have the same length and all angles the same size. This polygon has 2 sides the same length, not 3 sides the same length, so it cannot be regular.
What is the rate of change from x = 0 to x = pi over 2?
trig graph with points at 0, negative 4 and pi over 2, 0 and pi, 4 and 3 pi over 2, 0 and 2 pi, negative 4
Answer:
8/pi
Step-by-step explanation:
To find the rate of change from 0 to pi/2 we need the values at 0 and pi/2
f(0) = -4
f(pi/2) = 0
rate of change = change in f(x)/ change in x
= (f(x2) -f(x1))/( x2-x1)
= (0--4) / (pi/2 - 0)
= (0+4) / (pi/2)
= 4 / (pi/2)
= 8/pi
Oliver runs for 9 more minutes than Bobby.
The equation v = 9 + b, where v represents the number of minutes Oliver runs, and b represents the number of minutes Bobby runs, shows this relationship.
If Oliver runs 33 minutes, how many minutes does Bobby run?
A. 15
B. 42
C. 24
D. 51
Please answer quickly ill give Brainliest.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
Read two points from graph
y-intercept: (0, -3) → b= -3
x-intercept: (-2, 0).
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{0-(-3)}{-2-0}=\dfrac{3}{-2}=-\dfrac{3}{2}[/tex]
Therefore we have the equation of a line in slope-intercept form:
[tex]y=-\dfrac{3}{2}x-3[/tex]
Convert to the standard form [tex]Ax+By=C[/tex]
[tex]y=-\dfrac{3}{2}x-3[/tex] multiply both sides by 2
[tex]2y=-3x-6[/tex] add 3x to both sides
[tex]3x+2y=-6[/tex]
Answer: 3x + 2y = -6Answer:
y=mx+b
Step-by-step explanation:
Identify the values of the variables. Give your answers in simplest radical form. PLEASE HELP!!
Answer:
2 sqrt(3) = n
k = 4 sqrt(3)
Step-by-step explanation:
We know that cos 30 = adjacent/ hypotenuse
cos 30 = 6 /k
Multiply each side by k
k cos 30 = 6k * k
k cos 30 = 6
Divide each side by cos 30
k cos 30/ cos 30 = 6/ cos 30
k = 6 / cos 30
k = 6/ (sqrt(3)/2)
k =12 / sqrt(3)
We cannot leave the sqrt in the denominator
k = 12 / sqrt(3) * sqrt(3)/sqrt(3)
k = 12 sqrt(3)/3
k = 4 sqrt(3)
We know tan 30 = opposite/adjacent
tan 30 = n/6
Multiply each side by 6
6 tan 30 = n
6 * (sqrt(3)/3) = n
6/3 * sqrt(3) = n
2 sqrt(3) = n
The correct option is d. The values are 2 sqrt(3) = n, k = 4 sqrt(3)
We know that cos 30 = adjacent/ hypotenuse
Multiply each side by k
k cos 30 = 6k * k
k cos 30 = 6
Divide each side by cos 30
k cos 30/ cos 30 = 6/ cos 30
k = 6 / cos 30
k = 6/ (sqrt(3)/2)
k =12 / sqrt(3)
We cannot leave the sqrt in the denominator
k = 12 / sqrt(3) * sqrt(3)/sqrt(3)
k = 12 sqrt(3)/3
k = 4 sqrt(3)
We know tan 30 = opposite/adjacent
tan 30 = n/6
Multiply each side by 6
6 tan 30 = n
6 * (sqrt(3)/3) = n
6/3 * sqrt(3) = n
2 sqrt(3) = n