Step-by-step explanation:
[tex]\triangle{ABC}[/tex] is similar to [tex]\triangle{ADE}[/tex] so we can write the ratio
[tex]\dfrac{x}{6+4} = \dfrac{2}{6}[/tex]
Solving for x, we get
[tex]x = \left(\dfrac{2}{6}\right)(10) = \dfrac{10}{3}[/tex]
At Joe's Restaurant, 80 percent of the diners are new customers (N), while 20 percent are returning customers (R). Fifty percent of the new customers pay by credit card, compared with 70 percent of the regular customers. If a customer pays by credit card, what is the probability that the customer is a new customer?
Answer:
0.7407 = 74.07% probability that the customer is a new customer.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Pays by credit card
Event B: New customer.
Probability of a customer paying by credit card:
50% of 80%(new customers).
70% of 20%(regular customers). So
[tex]P(A) = 0.5*0.8 + 0.7*0.2 = 0.54[/tex]
Probability of a customer paying by credit card and being a new customer:
50% of 80%, so:
[tex]P(A \cap B) = 0.5*0.8 = 0.4[/tex]
What is the probability that the customer is a new customer?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4}{0.54} = 0.7407[/tex]
0.7407 = 74.07% probability that the customer is a new customer.
find two factors of the first number such that their product is the first number and their sum is the second number.
70,17
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Answer:
7, 10
Step-by-step explanation:
It often works well to look at the factor pairs that form the product.
70 = 1×70 = 2×35 = 5×14 = 7×10
The sums of these are 71, 37, 19, 17. The last pair of factors is the one of interest:
7 and 10.
If f(x) = x
2−3x+1
x−1
find f(-1) and f(-3)
Answer:
f(-1) = 2-3(-1) +1
= 7
f(-3)= 2-3(-3)+1
= 12
f(-1) = -1-1
= -2
f(-3) = -3-1
= -4
Why lines e and f must be parallel
a.
What is 46.7% of
4/5?
Answer:
0.3736
Step-by-step explanation:
46.7 percent of [tex]\frac{4}{5}[/tex] is 0.3736.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.What is a fraction?A number is stated as a quotient in mathematics when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.Solution -To find 46.7% of [tex]\frac{4}{5}[/tex].
So,
[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]
[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]
⇒ [tex]0.3736[/tex]
Therefore, 46.7% of [tex]\frac{4}{5}[/tex] is 0.3736.
Know more about percentages here:
https://brainly.com/question/24304697
#SPJ2
What is the other dimension of the rectangular cross section that is perpendicular to the base (the face that is shaded) and passes through the midpoints of the 10 cm edges?
________ centimeters by 18 centimeters
PLZ PLZ HELP
A rectangular prism with length of 10 centimeters, width of 8 centimeters, and height of 18 centimeters.
A. 2
B. 8
C. 10
D. 18
Which equation represents the parabola with focus (8, 4) and vertex (8, 2)
Answer:
Step-by-step explanation:
The focus lies above the vertex, so the parabola opens upwards.
suppose two soccer teams consist of players with a combined average height of 66 inches. if team a has an average height of 68 inches and has twice as many members as team b, what is the average height of team b
Answer:
The average height of team b is 62 inches.
Step-by-step explanation:
Mean:
The mean of a data-set is the sum of all values in the data-set divided by the number of values, that is:
[tex]M = \frac{s}{n}[/tex]
Sum:
Team a: Mean of 68 inches, 2x members.
Team b: Mean of y inches, x members.
So
[tex]s = 68*2x + yx = x(136 + y)[/tex]
Number of athletes:
[tex]n = 2x + x = 3x[/tex]
What is the average height of team b?
[tex]66 = \frac{x(136+y)}{3x}[/tex]
[tex]66 = \frac{136 + y}{3}[/tex]
[tex]136 + y = 198[/tex]
[tex]y = 198 - 136 = 62[/tex]
The average height of team b is 62 inches.
3. line has undefined slope and passes through (1,8)
Answer: x = 1
Step-by-step explanation:
(any line with an undefined slope is a vertical line)
x = 1 has an undefined slope and passes through (1,8)
The diameter of the circle is 2”. What is the area of the circle
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
1. 2/2 =1 1 is the radius
2. [tex]A = \pi r^2[/tex]
3. [tex]A=\pi 1^2[/tex]
4. [tex]A=\pi[/tex]
Determine if the sequence below is arithmetic or
geometric and determine the common difference / ratio in
simplest form.
3, 8, 13, ..
(PLEASE HELPP)
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Answer:
arithmetic; common difference of 5
Step-by-step explanation:
It usually works well to check differences first. Here, they are ...
8 -3 = 5
13 -8 = 5
These are the same value, so the sequence is arithmetic with a common difference of 5.
Two minor league baseball players got a total of 390 hits. Washington had 2 more hits than Sanchez. Find the number of hits for each player.
Washington had
hits. Sanchez had
hits
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Answer:
Washington had 196 hitsSanchez had 194 hitsStep-by-step explanation:
Let s represent the number of hits Sanchez had. Then Washington had (s+2) hits, and their hit total was ...
s +(s+2) = 390
2s = 388 . . . . . . subtract 2
s = 194 . . . . . . . . divide by 2
Sanchez had 194 hits; Washington had 196.
What is the value of x?
Answer:
Step-by-step explanation:
(2x - 5)° + 45° = 180°
2x - 5 + 45 = 180
x = 70
Find mBFE, help ASAP!!!
Answer: C
<BFE is 148 degrees
Step-by-step explanation:
We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?
1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same
2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.
3. Now, we have all the angles we need to find out <BFE.
4. <BFC+<CFD+<DFE=<BFE
5. Substitute to get
57+34+57=<BFE
91+57=<BFE
148=<BFE
6. Now we know that the answer is 148 degrees.
Pls answer , If you do tysm
Answer:
Step-by-step explanation:
ypu bhave to mulitply each by a percentage, for example, the percentage it says you mulitply it by
Ming rented a bike from Ted's Bikes. It cost $13 plus $3 per hour. If Ming paid $31,
then he rented the bike for how many hours?
A)7.
B)10.3333
C)6
D)10
Answer:
C, 6
Step-by-step explanation:
31-13 is 18, 18/3 is 6.
Answer:
6
Step-by-step explanation:
31-13= 18
18÷3 = 6
Answer from Gauthmath
WILL GIVE BRAINLIEST!!!! Write the following as an EXPRESSION: How much water do I need to add to l liters of pure alcohol to obtain a solution of 45% alcohol?
Answer:
If you add 690 ml of water you will obtain 1.690 liter of 70% alcohol. Of course if you halve the amounts, e.g. 0.5 liter 75% alcohol and 345 ml of water, you will also obtain 45% alcohol solution.
Peter, Jan, and Maxim are classmates. Their total score for the last test was 269. Peter's score was more than the sum of Jan's and Maxim's scores. What could be Peter's least possible score?
Answer:
135
Step-by-step explanation:
Given that :
Total score obtained by Peter, Jan and Maxim = 269
Let :
Peter's score = x
Jan's score = y
Maxim's score = z
x + y + z = 269
x > (y + z)
For x to be greater Than y + z ;
Then x > (269 / 2) ; x > 134.5
The least possible x score is 135
Hence, Peter's least possible score is 135.
A shop is having a sale.
All items are reduced by 25%
Work out the sale price of an item normally priced at £90
Answer:
£67.50
Step-by-step explanation:
You can divide 90 by 4 and then multiply your answer by 3 to get your final answer.
Hope this helps c:
What is the index of the radical below?
√10
A. 5
B. 9
C. 2
D. 10
2. What is the variable in the expression:
13x3 +7
(Select one answer)
7
3
13
Find the amount of tax and the selling price
Answer:
$71.415 or $71.42 is the selling price and the taxing is 1
Step-by-step explanation:
This is because I just rounded that extra 5 to make the 41 cents into 42 cents also y=79.35(.9) is the equation you needed to solve so just put 79.35(.9) into a calculator and you'll get 71.415 also 10% turns into a decimal 0.10 and then you subtract it from 1 as a whole and you'll get 0.9. I'm not really a mathmatician but I just got done learning this so I know what to do.
16. write an inequality for each graph
a.....
b.....
17. Graph each inequality on a number line.
a.....
b....
Answer:
Question 16
(a) x < 1 : the values of x are smaller than than 1 (e.g. possible values are 0, -1, -2, etc) and since the circle is not shaded it means that 1 isn't a possible value of x
(b) x [tex]\geq[/tex] -2 : the circle is filled therefore -2 is included in the answer
Question 17
(a) unfilled dot above -2 and arrow pointing to the left
(b) shaded circle above 4 with and arrow pointing to the right →
Martha ran a 3-mile race in 24 minutes. how long does it take her to run 1 mile?
Answer:
8 minuets
Step-by-step explanation:
24min/3miles = 8
Answer:
8 minutes.
Step-by-step explanation:
If we divide 24 minutes by 3 miles, your answer will be 8 minutes.
Find the perimeter of a triangle with sides 2 ft 3 in., 3 ft 4 in., and 4 ft 6 in.
A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50
Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]
7 over 50, which means that [tex]k = 7[/tex]
10 were dismissed, which means that [tex]n = 10[/tex]
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]
0.055 = 5.5% probability that exactly 5 employees were over 50.
if two of the three points (0,0) ,(2,3) (3,4) lie on one side and other on another side of line x-3y+3
Answer:
Opposite sides
Step-by-step explanation:
Given equation of line is
L=3x−2y+1=0
For the point (2,1), L=5>0
For the point (−3,5),L=−18<0
Opposite signs shows that the two points lies on the opposite side of the line L=0.
In a process control study, the overall process average over 15 samples is 63.45 with an average corresponding range of 5.6. What is the lower control limit of the R-chart
Answer:
[tex]LCL=1.94[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=15[/tex]
Mean [tex]\=x=63.45[/tex]
Range [tex]R=5.6[/tex]
Generally at [tex]n=15[/tex]
Value of Control chart constant,
[tex]LCL=D*R[/tex]
Generally the equation for Lower Control Limit is mathematically given by
[tex]LCL=D*R[/tex]
[tex]LCL= 0.347*5.6[/tex]
[tex]LCL=1.94[/tex]
❤✔
PLEASE HELP ME MAKE SURE YOUR ANSWER IS RIGHT BEFORE ANSWERING
Answer:
Always. Always.
Step-by-step explanation:
All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
Answer:
x=4
Step-by-step explanation:
[tex]\frac{16}{12}= \frac{6x}{5x-2}[/tex]
assuming that the triangles are similar, we can create this ratio of 16 or 12+4 to 6x and 12 to 5x-2
we can cross multiply to get 16(5x-2)=6x(12)
that leaves you with 80x-32=72x
we can then subtract 80x to both sides to get -32= -8x
solve by diving -8 from both sides which means that x=4
Answer:
[tex]this \: triangles \: are \: similar \: so \\ sides \: must \: be \: in \: a \: ratio \\ \frac{16}{12} = \frac{6x}{5x - 2} \\ \frac{4}{3} = \frac{6x}{5x - 2} \\ 4(5x - 2) = 3 \times 6x \\ 20x - 8 = 18x \\ x \: terms \: togather \\ 20x - 18x = 8 \\ 2x = 8 \\ x = \frac{8}{2} \\ x = 4 \\ thank \: you[/tex]
