Both planes have the same normal vector:
[tex]6x-y-z=6\implies\mathbf n=\langle6,-1,-1\rangle[/tex]
The plane we want must contain the point (4, -3, -1), so its equation would be
[tex]\mathbf n\cdot\langle x-4,y+3,z+1\rangle=0[/tex]
[tex]\implies 6(x-4)-(y+3)-(z+1)=0[/tex]
[tex]\implies\boxed{6x-y-z=28}[/tex]
Given A is between Y and Z and YA= 14x, AZ= 10x, and YZ= 12x + 48, find AZ
Answer:
96
Step-by-step explanation:
The value of AZ will be 40.
A is a point between Y and Z and YA = 14x , AZ = 10x and YZ = 12x + 48.
We have to calculate the value of AZ.
What is the value of MP , if N is the midpoint of M and P ?
The value of MP will be equal to the summation of NM and NP i.e., MP = NP + NM .
As per the question ;
A is the midpoint of Y and Z.
⇒ AZ + YA = YZ
⇒ 10x + 14x = 12x + 48
⇒ 24x = 12 x + 48
⇒ 12x = 48
⇒ x = 4
So ,
The value of AZ will be ;
AZ = 10 × 4
AZ = 40
Thus , the value of AZ will be 40.
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5. The Robin's Nest Nursing Home had a fundraising goal of $9,500. By the
end of the fundraiser, they had exceeded their goal by $2,100. How much
did they raise?
−2(2x + 5) − 3 = −3(x − 1)
Answer:
x =-16
Step-by-step explanation:
[tex]-2(2x + 5) - 3 = -3(x -1)[/tex]
Expand
[tex]\mathrm{Expand\:}-2\left(2x+5\right)-3:\quad -4x-13\\\\\mathrm{Expand\:}-3\left(x-1\right):\quad -3x+3\\\\-4x-13=-3x+3[/tex]
Collect like terms and simplify
[tex]-4x+3x =3+13\\-x =16\\[/tex]
Divide both side by -1
[tex]\frac{-x}{-1}=\frac{16}{-1}\\\\x =-16[/tex]
You are trying to estimate the average amount a family spends on food during a year. In the past the standard deviation of the amount a family has spent on food during a year has been approximately $900. If you want to be 99% sure that you have estimated average family food expenditures within $50, how many families do you need to survey? Round your answer up to the nearest whole number, if necessary.
Answer:
the number of families needed for the survey is 2,157
Step-by-step explanation:
The computation of the number of families needed for the survey is shown below:
Given that
The Standard deviation is $900
Service level = 99%
z value at 99% = 2.58
Expenditures = $50
Based on the above information
The number of families needed for the survey is
[tex]n = (\frac{zs}{E})^2\\\\= (\frac{2.58\times 900}{50})^2[/tex]
= 2,157
Hence, the number of families needed for the survey is 2,157
Simon used 13 pears and 9 apple to make fruit salad. What was the ratio of the number of apple to the number of fruit in the fruit salad?
Answer:
13:9
Step-by-step explanation:
The ratio of the number of apples to the number of fruits in the fruit salad is given by the equation A = 9 : 22
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the ratio of number of apples to the number of fruits be A
Now , the proportion will be
The number of pears = 13 pears
The number of apples = 9 apples
Now , the number of fruits = number of pears + number of apples
Substituting the values in the equation , we get
The number of fruits = 13 + 9 = 22
Now , the proportion of apples to fruits A is
Ratio of the number of apples to the number of fruits in the fruit salad A = number of apples : number of fruits
Substituting the values in the equation , we get
Ratio of the number of apples to the number of fruits in the fruit salad
A = 9 / 22
A = 9 : 22
Therefore , the value of A is 9 : 22
Hence , the proportion is 9 : 22
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What is the most appropriate measurement of the amount of liquid in Starpoint's pool?
A. ML.
B. KL.
C. CL.
D. Cg.
Answer: B. KL.
Step-by-step explanation:
A kiloliter (kl) is a unit which is derived from the metric SI (System International). This measurement is used when unit of volume with sides equal to one meter (1m) and as such, is equivalent to one cubic meter. One kiloliter (1kl) is which is same as one thousand liters (1000l). The kiloliter is used when volume of liquid is to be measured. This applies to a pool in the question.
The average cost of an item is defined as the total cost to produce divided by the number produced.A shoe company that pays $240,000 in rent and employee salaries per year figures it also must pay $3.50 in materials per shoe set it produces Write the equation needed to solve the problem. Use the equation to find the number of shoe sets the company would need to produce for the average cost of each set to be $7.50. Work out the problem, show all of your steps, and provide explanations.
Answer:
Step-by-step explanation:
Average cost = Total cost to produce / number of items produced
Fixed cost per year = $240,000
Variable cost = $3.50s
Where s = number of shoes produced
Total cost= fixed cost + variable cost
Total cost = $240,000 + $3.50s
When average cost = $7.50
Average cost = Total cost to produce / number of items produced
7.50 = $240,000 + $3.50s / s
Cross product
7.50s = $240,000 + $3.50s
Collect like terms
7.50s - 3.50s = 240,000
4s = 240,000
divide both sides by 4
s = 240,000 / 4
= 80,000
s = 80,000
The Pham family and the Morgan family each used their sprinklers last summer. The water output rate for the Pham family's sprinkler was 25L per hour. The water output rate for the Morgan family's sprinkler was 35L per hour. The families used their sprinklers for a combined 65total of hours, resulting in a total water output of 1975L . How long was each sprinkler used?
Answer:
Pham Family = 30 hours
Morgan Family = 35 hours
Step-by-step explanation:
Step 1 Deriving the equation
Let the duration in hours of Pham Family sprinkler = "x"
Let the duration in hours of Morgan Family = "y"
Total combined duration = 65 hours provided.
That is:
x + y = 65 Equation 1
Pham's sprinkler capacity = 25 litre per hour
Total water through this = 25 litre per hour for "x" hours = 25x
Morgan's sprinkler capacity = 35 litre per hour
Total water through this = 35 litre per hour for "y" hours = 35y
Now, provided
Total water output from both = 1,975 litre
That means
25x + 35y = 1,975 Equation 2
Step 2 Solving the equation
Let us multiply equation 1 with 25
We have
25x + 25y = 65 [tex]\times[/tex] 25
25x + 25y = 1,625 Revised Equation 1
Subtracting revised equation 1 from equation 2 we have:
(25x - 25x) + (35y - 25y) = (1,975 - 1,625)
0 + 10y = 350
y = 350/10 = 35
Since y = 35
Putting value of y in original equation 1 we have
x + 35 = 65
x = 65 - 35 = 30
Thus, Total Sprinkler hours of Pham = 30
Total Sprinkler hours of Morgan = 35
What are the graphs to these?
Answer:
The graph is in the image
Step-by-step explanation:
[tex]y = \frac{3}{5} x -3\\\\2x -y =-4\\\\y=-6,\:x=-5\\[/tex]
i already know the answer, its increasing by 4 but i dont know how to write the answer.
Answer: m+3
Step-by-step explanation:
Since the jump from each number increases by 3, you would write m+3, since m is indicated in the pattern.
4 - m/2 = 10
Please help!!
Answer:
M=3
Step-by-step explanation:
4-m/2=10subtract 4 from each sideget m/2=6then divide 2 from 6 and get m=3Hope this helps:)
choose all the expression with a difference less than 5
8.3
- 4.07
9.33
-3.99
7.1
- 2.603
12.3
- 7.08
7.005
- 2.005
Answer:
a and c
a and c are the expressions with a difference less than 5
Step-by-step explanation:
a) 8.3-4.07=4.23
b) 9.33-3.99=5.34
c) 7.1-2.603=4.497
d) 12.3-7.08=5.22
e)7.005-2.005=5
Hope this helps ;) ❤❤❤
Write the following set using roster notation. Do not include repeats.
A is the set of odd integers between 4 and 12.
Answer:
The Set of Natural Numbers: {1, 2, 3, 4, 5, . . .}
The Set of Whole Numbers: {0, 1, 2, 3, 4, 5, . . .}
The Set of Integers: {. . . , −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, . . .}
Step-by-step explanation:
Phone numbers in Italy are in the format AB-CDDD-XXXX and have the following conditions · A can be any number 3-9 · B can be any number 4-9 · C can be any number 5-9 · D can be any number 1-7 · X can be any number 0-9 How many total phone numbers can the Italians have? Question 4 options: 720,300,000 phone numbers 823,200,000 phone numbers 102,900,000 phone numbers 16,800,000 phone numbers
Answer:
Hey there!
A: 7
B: 6
C: 5
D: 7
X: 10
7x6x5x7x7x7x10x10x10=720,300,000
Let me know if this helps :)
Select the relationship that does represent a function
the 4th one is a relationship that is a fuction I think
Answer:
4th image
Step-by-step explanation:
the others cannot be functions since one domain cannot be in two ranges
A lamppost casts a shadow of 18 ft when the angle of elevation of the Sun is 33.7 degrees. How high is the lamppost? Round to the nearest foot
Answer:
12 feet or 12 ft
Step-by-step explanation:
We solve for this question using Trigonometric function of Tangent
tan θ = Opposite/ Adjacent
θ = Angle of elevation = 33.7°
Opposite side = Height of the lamp = ??
Adjacent side = Shadow of the lamp = 18 feet
Hence,
tan 33.7° = Opposite/ 18
tan 33.7° × 18 = Opposite
Opposite = 12.004507735 feet
Approximately to the nearest foot = 12.0feet
The height of the lamppost with a shadow of 18 ft. is 12 feet.
Trigonometric ratio
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let h represent the height of the lamppost, hence:
tan(33.7) = h/18
h = 12 feet
The height of the lamppost with a shadow of 18 ft. is 12 feet.
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33
56
Find the unknown side length, x. Write your answer in simplest radical form.
A 2047
B. 60
С.
5169
D. 65
Answer:
D. 65Step-by-step explanation:
The question lacks the appropriate diagram. Find the diagram attached.
The triangle is a right angled triangle that is made of of three sides namely the opposite, the adjacent and the hypotenuse (the longest side). According to the diagram, the longest side is the side with length x. To get the side length x, we will use the Pythagoras theorem as shown;
hyp² = opp²+adj²
hyp² = 33²+56²
x² = 1089+3136
x² = 4225
take the square root of both sides
√x² = √4225
x = 65
Hence the unknown side length x is 65
If the ratio of boys to girls at the school is 2:5 and there are 40 boys how many girls are there?
Answer:
100 girls
Step-by-step explanation:
The ratio of boys : girls is 2 : 5.
In other words, boys are 2 parts of the school while girls are 5 parts of the school.
Since there are 40 boys, 2 parts of the school is 40. Thus:
[tex]2p = 40\\p = 20[/tex]
1 part is 20.
Since there are 5 parts girls, there are
[tex]5p = 5*20 = 100[/tex]
100 girls.
Answer: 100 girls
The total number of students in school is 140 and number of girls at the school is equal to 100.
What do you mean by ratio ?
Ratio is the quantitative relationship between two values indicating how frequently one value contains or is contained within the other.
It is given that the ratio of boys to girls at the school is 2:5.
Let's assume the total number of students in school is x.
We now need to find the number of girls in the school but before that we must try to find the total number of students in the school.
Sum of ratios = 2 + 5 = 7
It is given that there are 40 boys in students.
2/7 of the total number of students are boys.
i.e., the expression can be written as :
2x / 7 = 40
2x = 40 × 7
2x = 280
x = 140
The total number of students in school is 140.
So , the number of girls in school is :
= 140 - 40
= 100
There are 100 girls in the school.
Therefore , the total number of students in school is 140 and number of girls at the school is equal to 100.
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There are 20 triangles and 4 squares. What is the simplest ratio of squares to total shapes
Answer:
1/6
Step-by-step explanation:
Given:
Number of squares = 4Number of triangles = 20Total
Number of total shapes = 20 + 4 = 24Ratio of squares to total shapes:
4/24 = 1/6Answer:
1:6
Step-by-step explanation:
There are 20 triangles and four squares, so we know the first part of the ratio is 4. The total number of shapes is 24, so we get 4:24, and if we simplify, we then get 1:6.
Hope this helps!
Proportional ratios are like equivalent fractions, but
Answer:
what is the question?
Step-by-step explanation:
What number belongs in the box to make the equation true? 2 7 3 5
n engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 9 engines and the mean pressure was 5.7 pounds/square inch with a variance of 0.81. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
Answer:
The calculated t- value = 1.11 > 2.89 at 0.025 level of significance
Null hypothesis is rejected
The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4
Step-by-step explanation:
Step(i):-
Given mean of the Population (μ) = 5.4
Given sample size 'n' = 9
Mean of the sample (x⁻) = 5.7
Standard deviation of the sample (s) = 0.81
Step(ii):-
Null Hypothesis: H₀: The engineer designed the valve such that it would produce a mean pressure of 5.4
H₀: μ = 5.4
Alternative Hypothesis : H₁: μ ≠ 5.4
Level of significance = 0.025
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{5.7 -5.4}{\frac{0.81}{\sqrt{9} } }[/tex]
t = 1.11
Degrees of freedom
ν = n-1 = 9-1 =8
t₀.₀₁₅ , ₈ = 2.89
The calculated t- value = 1.11 > 2.89 at 0.025 level of significance
Null hypothesis is rejected
The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4
What is 78 divided by 4.68
Answer:
16.67
Step-by-step explanation:
78 / 4.68
= 7800 / 468
= 16.67
When 78 is divided by 4.68 it gives 16.67 as a result.
DivisionFrom the four basic operations of arithmetic, the division is one. The division is generally done when we want to distribute something in equal portions.
therefore, 78 divided by 4.68 can be solved as,
Given to us78 divided by 4.68
[tex]78\div 4.68\\\\=\dfrac{78}{4.68}\\\\=\dfrac{78}{\dfrac{468}{100}}\\\\\\=\dfrac{78 \times 100}{468}\\\\=\dfrac{7800}{468}\\\\=16.6667 \approx 16.67[/tex]
Hence, when 78 is divided by 4.68 it gives 16.67 as a result.
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Simplify the following:
1.4 : 0.21
best answer gets brainliest.
Answer:
1.4/0.21= 140/21= 20/3
Step-by-step explanation:
Answer:
20:3
Step-by-step explanation:
decimal points can't be ratios so we have to convert to whole numbers:
so 1.4:0.21 becomes:
140:21
after simplifying fully( i divided both sides by 7) we come to 20:3.
Please help. I’ll mark you as brainliest if correct!
One leg of a right triangle has a length of 3 m. The other sides have lengths that are consecutive integers. Find these lengths.
The other leg is ___ m.
Answer:
The other leg is 4 m long, and the hypotenuse is 5 m long
Step-by-step explanation:
Recall that the longest side of a right angle triangle is its hypotenuse, and that the legs and hypotenuse must verify the Pythagorean identity:
[tex]hyp^2=leg_1^2+leg_2^2[/tex]
so, we know that the other two sides have consecutive integers for lengths. That is: if one is "x" in length, the other one must be "x+1"
So we can assume that the largest of this is the hypotenuse: "x+1"
Not, they must verify the Pythagorean identity:
[tex]hyp^2=leg_1^2+leg_2^2\\(x+1)^2=x^2+3^2\\x^2+2\,x+1=x^2+9\\2\,x+1=9\\2\,x=8\\x = 4[/tex]
then, the other side is of length 4 m, and finally the hypotenuse is of length 4+1 = 5 m
While riding her bike to the ocean and back home 6 times, Mandi timed herself at 52min, 54min, 53min, 51min, 53min, and 43min. She had set a goal of averaging 51 minutes for her rides. How many minutes will she need to spend on her seventh ride to attain her goal?
Answer:
306 min
Step-by-step explanation:
Please answer the last conversion !! 531 ms to s
Answer:
0.531 s
Hope it helped u if yes mark me BRAINLIEST
Find the LCM and HCF.
(a) p3 + 8 and p2 - 4
Answer:
In bold below.
Step-by-step explanation:
p^2 - 4 = (p - 2)(p + 2)
Note that 8 = 2^3 so
p^3 + 8 = ( p + 2)(p^2 + 4 - 2p)
So The HCF is p + 2.
The LCM = (p + 2)(p - 2)(p^2 + 4 - 2p)
Evaluate the expression when a=2 and b=20
What are the coordinates of B if the midpoint of line segment AB is (2,-5) and the coordinates of point A is (4,4)?
Answer:
i think it will be 20 unit diatance .