First set up the ratio 2/5 = 10/x where x is the number of girls.
Now, we can use cross-products to find the missing value.
So we have (2)(x) = (5)(10).
Simplifying, we have 2x = 50.
Dividing both sides by 2, we find that x = 25.
So there are 25 girls in the class if there are 10 boys.
Lynn invites some friends for lunch she needs to cater for 24 people. She decides to make pancakes. How many milk does Lynn need to use?
Answer: 900ml
Step-by-step explanation:
Recipe serves 4
Invited guests is 24 which is 6 x the recipe
6 x 150ml = 900ml
A quantity of (24xy) liters amount of milk is needed to cater 24 peoples.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have Lynn needs to cater for 24 people.
Assume that she intents to make [x] pancakes for each individual. And, in order to make 1 pancake, [y] liters of milk is needed. So, for a total of 24 people, she will make (24x) pancakes, that will need -
A{milk} = 24xy
Therefore, a quantity of (24xy) liters amount of milk is needed to cater 24 peoples.
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In the last 10 years, the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues, what will be the population in 10 more years? Round your answer to the nearest whole number.
Answer:
288750006
Step-by-step explanation:
Growth rate:
1.12% or 1.0112 timesCurrent population:
258,316,051Predicted population after 10 years:
258,316,051*(1.0112)^10 = 288,750,006.168≈ 288,750,006 roundedAnswer:288,929,825
Step-by-step explanation:
This is the right answer.
Prove the identity (sin3A+sinA)/2sin2A= cosA
Step-by-step explanation:
[tex] \frac{ \sin(3A) + \sin(A) }{2 \sin(2A) } [/tex]
Using the trigonometric identity
[tex] \sin(x) + \sin(y) = 2 \sin( \frac{x + y}{2} ) \cos( \frac{x - y}{2} ) [/tex]
Rewrite the expression
We have
[tex] \frac{2 \sin(2A) \cos(A) }{2 \sin(2A) } [/tex]
Reduce the fraction with 2
That's
[tex] \frac{ \sin(2A) \cos(A) }{ \sin(2A) } [/tex]
Reduce the fraction with sin 2A
We have the final answer as
cos AAs proven
Hope this helps you
The ratio of Ali's mass to John's mass is 6:5. The ratio of John's muss
to William's mass is 2: 3. Find the ratio of Ali's mass to William's mass.
(1) 1:2
(2) 2:1
(3) 4:5
(4) 5:4
Step-by-step explanation:
The ratio of Ali mass to Williams mass is
6 : 3
= 2 : 1
Option 2 is the correct answer
Name the sets of number to which each number belongs.
25/11
ON, R(natural, real numbers
O Q(rational numbers)
Q, R (rational, real numbers)
O W, R (whole, real numbers)
The correct answer is C. Q, R (rational, real numbers)
Explanation:
The number [tex]\frac{25}{11}[/tex] is a fraction, which means it represents proportions of a whole. This number can be classified as rational, which is represented by the letter Q because this category of numbers includes those numbers that can be represented as a fraction and the number provided is naturally a fraction. Moreover, this number is also a real number, which is a broad category of numbers represented by the letter R that includes rational numbers such as fractions. This means this number is rational and because of this, it is also real.
On the other hand, this number is not natural because this includes regular numbers such as 3, 43, or 3947 but not fractions, and it is not a whole number because a fraction does not represent a whole number but just a proportion.
Trans wants to buy a bicycle that costs $192. He plans to save $6 each week . How many weeks will it take him to save enough money ?
Answer:
32 weeks
Step-by-step explanation:
Total amount = 192
Each week he saves = 6
Number of weeks = x
=> 6x = 192
=> 6x/6 = 192/6
=> x = 32
It will take 32 weeks for him to buy the bicycle.
Bill is paid a monthly salary of $7200. What is his Medicare tax withholding for January?
-Taxable wages & tips subject to Additional Medicare Tax withholding Total Advances Received From Filing Form(s) 7200 for the Quarter · 13g. Your Form 941 is due by the last day of the month that follows the end of the quarter
Step-by-step explanation:
18. Use Pascal's triangle to find the coefficients of the expanded polynomial (a + b)^3.
options:
A) 1 3 3 1
B) 1 2 1
C) 1 1
D) 1 4 6 4 1
Answer:
Step-by-step explanation:
Hello, let's compute the first lines of the Pascal's triangle.
1
1 1
1 2 1
1 3 3 1
So for this question,
[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]
And then, the correct answer is A.
Thank you
Using pascals triangle coefficients of the expanded polynomial (a + b )³ is 1 3 3 1. Option A is correct
What is the pascals triangle?it is the array(in triangle form) of numbers, starting with 1 on the uvertexvetex and with 1's tending down to the two sides of a triangle. Each number lies between two numbers and down to them, and every value is the addition of the two numbers present at the above adjacent.
( a + b )³ = a³ + 3 a² b + 3 b² a + b³
Pascal's triangle =
1
1 2 1
1 3 3 1
1 4 6 4 1
and so on
From the above triangle, it represents ( a + b )^n where every number represents the coefficient. As for the given question the n = 3 so the third row in the pascal triangle i.e. coefficients of the expanded polynomial ( a + b )³ is 1 3 3 1.
Thus, the coefficients of the expanded polynomial ( a + b )³ is 1 3 3 1.
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Every week, you spend $15.35 on coffee. There are 52 weeks in a year. How much money do you spend on coffee in a year?
Answer:
$798.20
Step-by-step explanation:
15.35 × 52 = 798.20
When Betsy Ross sewed the first American flag, the flag had an area of 27 square feet. If the base of the flag was 9 feet, what was the height of the flag?
Answer:
The height of the flag was 3 feet.
Step-by-step explanation:
To solve this problem, we must first recall the formula for area of a rectangle to be:
Area = base * height
Next, we can substitute in the values that we were given in the problem. We were told that the area was 27 square feet and the base was 9 feet.
27 = 9 * height
Now we can treat this equation that we have created similar to any other equation we would like to solve. We must solve for the unknown, or the variable, which in this case is the height. To do this, we should divide both sides by 9 to get the "height" variable by itself on the right side of the equation. This is modeled below:
27/9 = (9 * height)/9
3 = height
Therefore, the height of the flag was 3 feet.
Hope this helps!
Answer:
The height is 3,
Step-by-step explanation:
First up, if we know the B in the B*H=A formula, we can divide the area by the base (27/9) and get the height, 3.
I too am learning this. The thing is you want to do a reverse order. For example, 2*3=6; so automatically we would know that 6/3=2.
Hope this has helped!
:)
A 12 foot board is cut so that one piece is 5 times as long as the other. Find the length of each piece.
Answer:
2 and 10
Step-by-step explanation:
Let x be length of the small piece and y the length of the big one.
● y = 5x
Since the big piece is 5 times longer than the short one.
The total length is 12 ft
● y + x = 12
● 5x + x = 12
● 6x = 12
Divide both sides by 6
● 6x/6 = 12/6
● x = 2
So the length of the two pieces are 2 ft and 10 ft (5×2)
The length of each piece is 2 units and 10 units.
How to know how many times a number is to another ?To know how times a number is to another just divide the larger number to the smaller number.
According to the given question a 12 foot board is cut so that one piece is 5 times as long as the other.
Assuming one piece to be x and the other to be 5x.
∴ x + 5x = 12
6x = 12
x = 2.
So, one piece is of 2 units and other piece is of 5(2) = 10 units.
To confirm that one piece is of 5 times of the other we divide the larger piece by the smaller piece which is 10/2 = 5.
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Evaluate 1 1/3 + 2 2/5
Answer:
3 11/15
Step-by-step explanation:
Answer:
3 11/15
Step-by-step explanation:
the 1/3 and 2/5 cannot be added properly, so we must make the denominator the same for both sides. So we make it fifteen.
The new equation is: 1 5/15 + 2 6/15.
1 5/15 + 2 6/15 = 3 11/15.
hope this helps :)
Explain the error in simplifying the following
Answer:
1/3
Step-by-step explanation:
When simplifying the expression and x - 2 is eliminated there will be 1/3 left not 3
Hallar el conjunto solución de la siguiente inecuación: x^2-12x+36≤0
Answer:
x = 6
Step-by-step explanation:
x² - 12x + 36 ≤ 0
(x - 6)(x - 6) ≤ 0
(x - 6)² ≤ 0
x - 6 = 0
x = 6
es el único valor que cumple la condición, cualquier otro sera mayor que 0
In 2011, a U.S. Census report determined that 68% of college students are working students. A researcher thinks this percentage has changed and surveys 144 college students. The researcher reports that 93 of the 144 are working students. Is there evidence to support the researcher's claim at the 1% significance level
Answer:
We will fail to reject the null hypothesis and conclude that there is sufficient evidence not to support the researchers claim.
Step-by-step explanation:
We are given;
Population proportion; p = 68% = 0.68
Sample proportion; p^ = 93/144 = 0.6548
n = 144
The hypotheses are:
Null hypothesis;H0: p = 0.68
Alternative hypothesis;Ha: p ≠ 0.68
np = 144 × 0.6548 > 5 and nq = n(1 - p) = 144(1 - 0.68) > 5.
Since np and nq are more than 5, we can use the z-test .
z-formula in this case is;
z = (p^ - p)/√(p(1 - p))
Plugging in the relevant values, we have;
z = (0.6548 - 0.68)/√(0.68(1 - 0.6548))
z = -0.0252/0.4845
z = -0.052
From the z-table attached, we have a p-value of approximately 0.4801
P-value is higher than the significance level of 0.01.
Thus,we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the researchers claim.
Can the following be assumed from a diagram? The measures of angles
.2 CALCULATION Mr. Davis took a job through an employment agency. The job pays $88K per year. He must pay a fee to the employment agency. The fee is 22% of his first four weeks’ pay. How much money must Mr. Leonard pay the agency, to the nearest cent? K = 1,000 88K = 88 × 1,000 = __________ annual salary Weekly salary = annual salary ÷ 52 Weekly salary = 88,000 ÷ 52 = __________ 4 weeks salary = 4 × 1,692.31 = __________ 22% of 4 weeks salary = 6,769.24 × 0.22 ≈ __________ Mr. Leonard must pay the agency __________.
Answer: $1489.23 is the amount Mr. Leonard must pay to the agency, which is 22% of his 4-week salary of $6769.24.
This is assuming Mr. Davis and Mr. Leonard are the same person.
Fill in the blank answers: $88,000. $1692.31. $6769.24. $1489.23.
Estimate by rounding the divisor to the nearest tens place and the dividend to the nearest
compatible number. Then find the quotient.
Enter the remainder, if any, as a fraction in simplest form.
59 ) 5,613
The estimate is?
The quotient is?
Answer:
Estimate: 90
Quotient: 95
Remainder: 8/59
Step-by-step explanation:
1. What is the slope of the line through the points (-6, 3) and (-7, -4)?
o 1
Answer:
[tex] \boxed{ \bold{ 7}}[/tex]Step-by-step explanation:
Let the points be A and B
A ( -6 , 3 ) ⇒ ( x₁ , y₁ )
B ( -7 , -4 )⇒ ( x₂ , y₂ )
Now, let's find the slope:
[tex] \mathsf{\frac{y2 - y1}{x2 - x1}}[/tex]
Plug the values
⇒[tex] \mathsf{ \frac{ - 4 - 3}{ - 7 - ( - 6)} }[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
⇒[tex] \mathsf{ \frac{ - 4 - 3}{ - 7 + 6}} [/tex]
Calculate
⇒[tex] \mathsf{ \frac{ - 7}{ - 1} }[/tex]
Any expression divided by -1 equals it's opposite
⇒[tex] \mathsf{7}[/tex]
Hope I helped!
Best regards!!
For the statement below, write the claim as a mathematical statement. State the null and alternative hypotheses and identify which represents the claim. An amusement park claims that the mean daily attendence at the park is people. Write the claim as a mathematical statement. A. B. C. D. E. F. Choose the correct null and alternative hypotheses below. A. : : B. : : C. : : D. : : E. : : F. : : Identify which is the claim. A. The null hypothesis : is the claim B. The alternative hypothesis : is the claim C. The alternative hypothesis : is the claim D. The alternative hypothesis : is the claim. E. The null hypothesis : is the claim
The question is not complete, so i have attached it.
Answer:
A) Option B: μ ≤ 19,000
B) Option C:
H0: μ ≤ 19,000
Ha: μ > 19,000
C) Option D: The null hypothesis H0: μ ≤ 19,000 is the claim
Step-by-step explanation:
A) From the question, we are told that an amusement park claims that the mean daily attendence at the park is at most 19,000 people.
Now, since it's at most 19000 people, it means that they are either 19000 or less. So the claim is;
μ ≤ 19,000 which is option B
B) Now, the claim is usually the null hypothesis. Thus, the null hypothesis is;
H0: μ ≤ 19,000
While the alternative hypothesis which states the opposite of the claim is;
Ha: μ > 19,000
So, option C is the correct answer
C) The claim is μ ≤ 19,000
Now, this also happens to be the null hypothesis.
Thus, the null hypothesis H0: μ ≤ 19,000 is the claim.
So option D is correct.
In 2007, the first generation of the i-phone sold for $499. The average cost of an i-phone today is $999. At a press conference just outside a telephone museum in Cle Elum, WA, the CEO of Apple, Tim Cook, stated that the rise in cost is purely due to inflation. Use the Consumer Price Index to either verify or falsify Cooks’s statement. Is he wrong?
Answer: the statement made by Tim Cook is TRUE
Step-by-step explanation:
Given that;
in 2007 cost of 1st gen iphone = $499 (base year price)
cost of iphone today = $999 (current year price)
Using the Consumer Price Index
the Consumer Price Index = (cost pf product in current years/cost of product base year) × 100
we substitute
CPI = (999/499) × 100
CPI = 200.2004
so the CPI is 100.2004% higher in the current year than in the base year
Checking the inflation rate
IR = (( CPI this year- CPI last year)/CPI last year) × 100
CPI last year (base year) = 100
CPI current year is = 100.2004
so
IR = (( 100.2004 - 100)/100) × 100
IR = 0.002004 × 100
IR = 0.2004%
THEREFORE the statement made by Tim Cook is TRUE
i need help can someone help me please
Answer:
a. x=80
b. x=30
Step-by-step explanation:
Use the exterior angle theorem: as shown in the picture
# a
25+x=105
x=80
#b
2x+(3x+2)=152
5x+2=152
5x=150
x=30
A dishwasher is priced at $635.50. There is an 8% sales tax rate. What is
the sales tax for the dishwasher in dollars and cents?
i need this answer right away!!!
What is the critical value at the 0.05 level of significance for a goodness-of-fit test if there are six categories?
Answer:
The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07 (One tailed test )
Step-by-step explanation:
For n=6 the degrees of freedom will be n-1 = 5 .
The goodness of fitness test χ²with significance of level ∝= 0.05 and 5 degrees of freedom is 11.07 (One tailed test )
The critical region depends on ∝ and the alternative hypothesis
a) When Ha is σ²≠σ² the critical region is
χ² < χ²(1-∝/2)(n-1) and χ² > χ²(1-∝/2)(n-1) Two tailed test
( χ² < 0.83) and ( χ² > 0.83)
b) When Ha is σ²> σ² the critical region falls in the right tail and its value is
χ² > χ²(∝)(n-1) One tailed test {11.07 (One tailed test )}
c) When Ha is σ² <σ² the critical region will be entirely in the left tail with critical value
χ²(1-∝)(n-1) One tailed test (1.145)
Answer:
the newsar si evsenyt esventy
Step-by-step explanation:
chemist is using 332 milieters of solution of acid and water if 14.4% of the solution is acid how many milliliters of acid is there
Answer:
332*14.4% = 332*.144 = 47.808
Julio wants to purchase a truck. The purchase price of the truck is $ 38 , 000.00 The dealership will allow him to pay cash or finance the truck for a down payment of $ 5 , 000.00 and 60 monthly payments of $ 750.00. Julio chooses to finance the truck.
Answer:
88,000
Step-by-step explanation:
If the down payment is $5,000and the monthly payment is $750. Then the amount of the truck through finance is $50,000.
What is finance?The big-scale money management, particularly by governments or huge corporations.
Julio wants to purchase a truck.
The purchase price of the truck is $ 38,000.00.
The dealership will allow him to pay cash or finance the truck for a down payment of $ 5,000.00 and 60 monthly payments of $ 750.00.
Julio chooses to finance the truck.
If he makes the payment through finance. Then the amount of the money he has to pay will be
Amount = 5000 + 60 × 750
Amount = 5000 + 45000
Amount = $50,000
If he makes the payment through finance. Then the amount of money he has to pay is 50,000 dollars.
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Question 6(Multiple Choice Worth 1 points)
(01.02 LC
Solve for x: -3x - 3= -3(x + 1)
O All real numbers
O No solution
06
-6
HELP ME OUT ASAP
Answer:
-3x-3=-3(x+1)
opening the bracket and collecting like terms, we have
-3x+3x=-1+3
thus, no solution
half of 5/6. thanks
Answer: 41.665
Step-by-step explanation:
5/6 as a percent is 83.33.
83.33 divided by 2 equals 41.665.
So, the answer is 41.665.
Hope this helps!
Answer: 0.4166667
Explanation: Make 5/6 to 0.8333. Divide the decimal by 2.
Hope it helps!
lovelymoonlight
I understand the homework, but question 9. Could someone please help? This assignment is due on Friday (8/21/2020)
Answer:
I think B or C I'm not sure but I hope this helps!
Step-by-step explanation:
Find a formula for the sum of n terms. Use the formula to find the limit as n → [infinity]. lim n → [infinity] n 2 + i n 8 n i = 1
Complete Question
Find a formula for the sum of n terms. [tex]\sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )[/tex]
Use the formula to find the limit as [tex]n \to \infty[/tex]
Answer:
[tex]K_n = \frac{n + 73 }{n}[/tex]
[tex]\lim_{n \to \infty} K_n = 1[/tex]
Step-by-step explanation:
So let assume that
[tex]K_n = \sum\limits_{i=1}^n ( 8 + \frac{i}{n} )(\frac{2}{n} )[/tex]
=> [tex]K_n = \sum\limits_{i=1}^n ( \frac{16}{n} + \frac{2i}{n^2} )[/tex]
=> [tex]K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)[/tex]
Generally
[tex]\sum\limits_{i=1}^n (k) = \frac{1}{2} n (n + 1)[/tex]
So
[tex]\sum\limits_{i=1}^n (8) = \frac{1}{2} * 8* (8 + 1)[/tex]
[tex]\sum\limits_{i=1}^n (8) = 36[/tex]
[tex]K_n = \frac{2}{n} \sum\limits_{i=1}^n (8) + \frac{2}{n^2} \sum\limits_{i=1}^n(i)[/tex]
and
[tex]\sum\limits_{i=1}^n (i) = \frac{1}{2} n (n + 1)[/tex]
Therefore
[tex]K_n = \frac{72}{n} + \frac{2}{n^2} * \frac{1}{2} n (n + 1 )[/tex]
[tex]K_n = \frac{72}{n} + \frac{1}{n} (n + 1 )[/tex]
[tex]K_n = \frac{72}{n} + 1 + \frac{1}{n}[/tex]
[tex]K_n = \frac{72 + 1 + n }{n}[/tex]
[tex]K_n = \frac{n + 73 }{n}[/tex]
Now [tex]\lim_{n \to \infty} K_n = \lim_{n \to \infty} [\frac{n + 73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [\frac{n}{n} + \frac{73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 + \frac{73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = \lim_{n \to \infty} [1 ] + \lim_{n \to \infty} [\frac{73 }{n} ][/tex]
=> [tex]\lim_{n \to \infty} [\frac{n + 73 }{n} ] = 1 + 0[/tex]
Therefore
[tex]\lim_{n \to \infty} K_n = 1[/tex]