QUESTION 1
The given logarithm is
[tex]8\log_g(x)+5\log_g(y)[/tex]
We apply the power rule of logarithms; [tex]n\log_a(m)=\log_(m^n)[/tex]
[tex]=\log_g(x^8)+\log_g(y^5)[/tex]
We now apply the product rule of logarithm;
[tex]\log_a(m)+\log_a(n)=\log_a(mn)[/tex]
[tex]=\log_g(x^8y^5)[/tex]
QUESTION 2
The given logarithm is
[tex]8\log_5(x)+\frac{3}{4}\log_5(y)-5\log_5(z)[/tex]
We apply the power rule of logarithm to get;
[tex]=\log_5(x^8)+\log_5(y^{\frac{3}{4}})-\log_5(z^5)[/tex]
We apply the product to obtain;
[tex]=\log_5(x^8\times y^{\frac{3}{4}})-\log_5(z^5)[/tex]
We apply the quotient rule; [tex]\log_a(m)-\log_a(n)=\log_a(\frac{m}{n} )[/tex]
[tex]=\log_5(\frac{x^8\times y^{\frac{3}{4}}}{z^5})[/tex]
[tex]=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})[/tex]
Joes, who is the youngest member of the wrestling team at Northwood High school, is 5 years less than one-half the age of the coach. If the coach is n years old, which expression describes joe's age
1/2 n - 5 or (n/2) - 5
The correct expression which describes joe's age is,
⇒ 1/2n - 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Joes, who is the youngest member of the wrestling team at Northwood High school, is 5 years less than one-half the age of the coach.
Now, Let the coach is n years old.
Hence, We can formulate;
The correct expression which describes joe's age is,
⇒ 1/2n - 5
Thus, the expression which describes joe's age is,
⇒ 1/2n - 5
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1 4 of a pizza is split equally between 3 sisters. How much of a whole pizza will each sister get? A) 1 12 B) 1 3 C) 1 6 D) 1 7
Answer:
A. 1 12
Step-by-step explanation:
Mr. Lubec put her 28 students into four equal groups she gave each group 35 sheets of paper how many sheets of paper to each student get
Answer:
5 sheets.
Step-by-step explanation:
There are 28 / 4 = 7 students in one group.
Each group was given 35 sheets of paper so each student got 35/7
= 5 sheets.
Each student will get 5 sheets of paper. This is found by dividing the total number of sheets per group (35) by the number of students in each group (7).
Explanation:To solve the problem, we first need to understand that Mr. Lubec's 28 students are divided into four equal groups. We divide 28 by 4 to determine how many students are in each group, which is 7 students. Mr. Lubec gave each group 35 sheets of paper. To find out how many sheets of paper each student receives, we divide the total number of sheets per group by the number of students in each group.
So, we calculate 35 sheets ÷ 7 students, which equals 5 sheets of paper per student. Therefore, each student will get 5 sheets of paper.
Which of the tables would show inverse variation?
Answer:
C
Step-by-step explanation:
An inverse variation is where the product of inputs and outputs is constant. This means x*y is always the same number.
A is not a solution since it has 3*-4 = -12 and -2*4 = -8. It's not the same.
B is not a solution since it has 2*8 = 16 and 3*12 = 36. It's not the same.
C is a solution since 12*4 = 48 and 8*6 = 48 and 4*12 = 48 and 3*16 = 48. It's the same.
D is not a solution since it has 1*6 = 6 and 2*4 = 8. It's not the same.
A researcher wants to prove that there is a difference in the average life spans between men and women in Japan. Let mu1 = average life span of Japanese women and mu2 = average life span of Japanese men. A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years. A random sample of 10 men showed an average lifespan of 77 years, with a sample standard deviation of 6.4 years. Assume that life spans are normally distributed and that the population variances are equal. If alpha = .05 and the null hypothesis is mu1 – mu2 = 0, what is (are) the critical value(s) for the hypothesis test?
Answer:
t < -2.101, and t > 2.101
Step-by-step explanation:
We are running a hypothesis for the difference of 2 sample means, assuming normality, and assuming that population variances are equal. This determines which test we run.
We have:
Sample 1: (women)
n = 10
x = 83
s = 7
Sample 2: (men)
n = 10
x = 77
s = 6.4
The hypothesis for the test are:
H0: µ1 - µ2 = 0
Ha: µ1 - µ2 ≠ 0
The significance level is 5%. The degrees of freedom is 2 less than the sum of the sample size, in this case, 18. Our t-value is: 2.101
Our critical values for the test statistic are: t < -2.101, and t > 2.101
The critical value(s) for the hypothesis test if A random sample of 10 women showed an average lifespan of 83 years, with a sample standard deviation of 7 years is t < -2.101, and t > 2.101.
What is average?The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
In Sample 1: (women)
n = 10
x = 83
s = 7
In Sample 2: (men)
n = 10
x = 77
s = 6.4
The hypothesis for the test are:
H₀: µ1 - µ2 = 0
Hₐ: µ1 - µ2 ≠ 0
The significance level is 5%. The degrees of freedom is 2 less than the sum of the sample size, in this case, 18. Our t-value is: 2.101
Our critical values for the test statistic are: t < -2.101, and t > 2.101
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you put $634 into an investment at 6% compounded annually for six years. what will be the balance be at the end of six years?
Final answer:
The balance at the end of six years will be approximately $899.48.
Explanation:
To calculate the balance at the end of six years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^(nt)[/tex]
where A is the final amount, P is the principal amount (initial investment), r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
Plugging in the values, we have:
[tex]A = 634(1 + 0.06/1)^(1*6)[/tex]
[tex]= 634(1.06)^6[/tex]
= 634(1.418519)
= $899.48
Eric practice piano and guitar for 8 hrs. He practiced piano for 1 fourth of 8 hrs. How many hours did Eric practice the piano this week?
➷ Multiply the total value by 1/4:
1/4 x 8 = 2
He practiced it for 2 hours.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
2 hours.
Step-by-step explanation:
The time he practiced the piano = 1/4 * 8 = 2 hours.
Use the spinner to find each theoretical probability
P (a number no more than 5)
P (an even number)
P (a number less than 3)
An engineering professor acquires a new computer once every 2 years. the professor can choose from three models: m1, m1, and m3. if the present model is m1, the next model can be m2 with probability .2, or m3 with probability .15. if the present model is m2, the probabilities of switching to m1 and m3 are .6 and .25, respectively. and, if the present model is m3, then the probabilities of purchasing m1 and m2 are .5 and .1, respectively. represent the situation as a markov chain.
Final answer:
The engineering professor's choice of new computer models over time can be modeled using a Markov chain, with specific transition probabilities for moving between models M1, M2, and M3. These probabilities are used to construct a transition matrix that allows us to analyze the selection pattern.
Explanation:
The scenario described can be represented as a Markov chain, which is a mathematical system that undergoes transitions from one state to another, with probabilities that are dependent on the current state only. Here, we have three models, M1, M2, and M3, which represent the states of the Markov chain. The transition probabilities define how likely it is to move from one state to another.
To construct this Markov chain, we set up a probability matrix P where the rows represent the current state, and the columns represent the next state. For the given model:
If the current model is M1, we have transition probabilities of 0.2 to M2 and 0.15 to M3.
If the current model is M2, we have transition probabilities of 0.6 to M1 and 0.25 to M3.
If the current model is M3, we have transition probabilities of 0.5 to M1 and 0.1 to M2.
Since the probabilities must add up to 1, the probability of remaining in the same state is 1 minus the sum of transition probabilities to other states. With these probabilities, we can fill in the transition matrix P:
P(M2|M1) = 0.2, P(M3|M1) = 0.15, P(M1|M1) = 0.65.
P(M1|M2) = 0.6, P(M3|M2) = 0.25, P(M2|M2) = 0.15.
P(M1|M3) = 0.5, P(M2|M3) = 0.1, P(M3|M3) = 0.4.
By using this transition matrix, we can analyze the professor's behavior in selecting new computer models over time.
Big Smiles Toy Company needs to pack marbles into a box. The company has two boxes they can use. Box A is 9 inches wide, 13 inches long, and 11.5 inches high. Box B is 14 inches wide, 8.5 inches long, and 12 inches high. Big Smiles Toy Company wants to use the larger box. Which box should the company choose and how much larger is it?
Answer:
The answer is Box B by 82.5 inches, let me know if it helped.
Step-by-step explanation
The company should choose Box B as it is larger than Box A. The volume of Box A is 1,497.75 cubic inches and the volume of Box B is 1,428 cubic inches, making Box A 69.75 cubic inches larger than Box B.
Explanation:The company should choose Box B as it is larger than Box A. To calculate the size difference, we need to find the volume of each box, which is calculated by multiplying the length, width, and height of the box. For Box A, the volume is 9 inches * 13 inches * 11.5 inches = 1,497.75 cubic inches. For Box B, the volume is 14 inches * 8.5 inches * 12 inches = 1,428 cubic inches. Therefore, Box A is 69.75 cubic inches larger than Box B.
The friendly sausage factory (fsf) can produce hot dogs at a rate of 5,000 per day. fsf supplies hot dogs to local restaurants at a steady rate of 260 per day. the cost to prepare the equipment for producing hot dogs is $66. annual holding costs are 45 cents per hot dog. the factory operates 294 days a year.
a. find the optimal run size. (do not round intermediate calculations. round your answer to the nearest whole number.) optimal run size
b. find the number of runs per year. (round your answer to the nearest whole number.) number of runs
c. find the length (in days) of a run. (round your answer to the nearest whole number.)
Answer:
a. 21 327 hot dogs/run
b. 70 runs/yr
c. 4 da/run
Step-by-step explanation:
Data:
Production rate (p) = 5000/da
Usage rate (u) = 260/da
Setup cost (S) = $66
Annual carrying cost (H) = $0.45/hot dog
Production days (d) = 294 da
Calculations:
a. Optimal run size
(i) Annual demand (D) = pd = (5000 hot dogs/1 day) × (294 days/1 yr)
= 1 470 000 hot dogs/yr
(ii) Economic run size
[tex]Q_{0}= \sqrt{\frac{2DS }{ h}\times\frac{ p}{p-u }}[/tex]
[tex]= \sqrt{\frac{2\times1470000\times66 }{ 0.45}\times\frac{ 5000}{5000-260 }}[/tex]
[tex]= \sqrt{431200000\times\frac{ 5000}{4740 }}[/tex]
[tex]= \sqrt{454852321}[/tex]
= 21 327 hot dogs/run
b. Number of runs per year
Runs = D/Q₀ = (1 470 000 hot dogs/1yr) × (1 run/21 327 hotdogs)
= 70 runs/yr
c. Length of a run
Length = Q₀/p = (21 327 hot dogs/1 run) × (1 da/5000 hot dogs)
= 4 da/run
To find the optimal run size, use the EOQ formula and calculate the square root. Divide the annual demand by the optimal run size to find the number of runs per year. Finally, calculate the length of a run by dividing the days in a year by the number of runs per year.
Explanation:The optimal run size can be found using the Economic Order Quantity (EOQ) formula. EOQ = sqrt((2DS)/(H)) where D is the annual demand, S is the setup cost per order, and H is the holding cost per unit per year.
Using the given values:
D = 260 per day * 294 days = 76,440
S = $66
H = $0.45
EOQ = sqrt((2 * 76,440 * 66) / (0.45)) ≈ 6868
The optimal run size is approximately 6868 hot dogs.
The number of runs per year can be calculated by dividing the annual demand by the optimal run size:
Number of runs = 76,440 / 6868 ≈ 11.15
Since the factory operates 294 days a year, the number of runs per year is approximately 11.
The length of a run can be calculated by dividing the days in a year by the number of runs per year:
Length of a run = 294 / 11 ≈ 26.73
The length of a run is approximately 27 days.
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What is the slant height x of the square pyramid?
Express your answer in radical form.
Answer:
x = [tex] 4 \sqrt { 3 } [/tex]
Step-by-step explanation:
We are given a diagram of a pyramid with a right angled triangle which has [tex]30[/tex]°, [tex]60[/tex]° and [tex]90[/tex]° angles an the hypotenuse is [tex]8cm[/tex].
Since we have a right angled triangle, we can apply sin here:
We know that [tex]sin 60 = \frac{\sqrt{3} }{2}[/tex] so we can write it as
[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]
So we get the slant height of x = [tex]4\sqrt{3}[/tex].
Answer:
The slant height of square pyramid = 4√3 m
Step-by-step explanation:
From the figure we can see a square pyramid with lateral edge 8 m
Also the one angle of face triangle is 60° , therefore the face triangle is an equilateral triangle.
Therefore the base is 8 m
To find the slant height
slant height² = Lateral edge² - (base/2)²
= 8² - (8/2)² = 8² - 4²
= 64 - 16 = 48
Slant height = √48 = 4√3 m
Therefore slant height of square pyramid = 4√3 m
Which of the following is the general solution of the differential equation dy/dx equals the quotient of 8 times x / y ?
A.)y^2 = x^2 + C
B.)x^2 - y^2 = C
C.)x^2 = 4x^2 + C
D.)y^2 = 8x^2 + C
I believe the answer is D
The general solution of the differential equation [tex]\frac{dy}{dx} = \frac{8x}{y}[/tex] using variable separable method is [tex]y^{2}= 8 x^{2} +C[/tex].
What is variable separable method?If it is possible to write a differential equation by the transportation of terms, in the form f(x) dx = g(y) dy where f(x) is the function of x and g(y) is the function of y, then we say that variables are separable.
The solution is given by:
[tex]\int\ {f(x)} \, dx = \int\ {g(y)} \, dy + c[/tex]
where c is the arbitrary constant.
[tex]\frac{dy}{dx} = \frac{8x}{y} \\\\y\, dy = 8x \,dx\\\\\int\ {y} \, dy = \int\ {8x} \, dx\\\\\frac{y^{2} }{2} = \frac{8x^{2} }{2} + C \\\\y^{2}= 8 x^{2} +C[/tex]
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If 1 4 of a gallon of milk is shared equally between 6 friends, how much milk will each friend have?
1 Gallon = 4 quarts of milk
1/4 = 1 quart of milk
4 quarts of milk = 8 pints of milk
8/6 = 1.33 pints of milk
Each friend has 1.33 pints of milk
Each friend will get 1/24 of a gallon of milk.
To find out how much milk each friend will have, we need to divide 1/4 of a gallon by 6.
how much milk each friend gets,
(1/4) ÷ 6
(1/4) × (1/6)
= 1/24
Therefore, each friend gets 1/24 of a gallon of milk.
In conclusion, if 1/4 of a gallon of milk is shared equally among 6 friends, each friend will have 1/24 of a gallon of milk.
The circumference of a circle is 34π
find the diameter and radius
please put an explanation, I desperately need help with finding diameter/radius with circumference
The circumference of a circle is calculated like this:
[tex]c = 2 \times \pi \times r = \pi \times d[/tex]
If the circumference of the circle is 34π, its diameter is 34(cm), therefore its radius is 17(cm).
To find the diameter and radius of a circle when given the circumference, you can use the formulas C = 2πr or C = πd. In this case, the circumference is 34π. The circle's diameter is 34 units, and the radius is 17 units.
Explanation:To find the diameter and radius of a circle when given the circumference, you can use the formula C = 2πr or C = πd, where C is the circumference, r is the radius, and d is the diameter. In this case, the circumference is given as 34π. Using the formula C = πd, we can substitute the value of the circumference and solve for the diameter:
34π = πd
Dividing both sides of the equation by π, we get:
34 = d
So, the diameter of the circle is 34 units. To find the radius, we can use the formula r = d/2:
r = 34/2
r = 17
Therefore, the circle's diameter is 34 units, and the radius is 17 units.
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WILL GIVE BRAINLYEST
The Problem:
Ms. Chen is planning to take her camp group on a field trip to Pottery Bayou where each person will create her own piece of art pottery. The regular cost is $32 per person. There is a group special that costs $20 per person with an additional $84 fee for a private room. Ms. Chen is trying to decide if she should use the regular price or the group special.
Write an equation to show the total cost of the regular price with x people (8 points)
Write an equation to show the total cost of the group special with x people (8 points)
1) regular cost for one person is: 32 ×1 = $32
for X people it would be 32X as you should times by the number of people.
= 32x
2)1 person is (20×1) + 84
20 + 84 = $104
for X people it would be 20x + 84
= 20x + 84
Robbie, a structural engineer, will earn $64,000 his first year working for a commercial construction company with annual raises of 8%. What are his total earnings at the end of 5 years?
Answer:
Total earnings at the end of 5 years
= $87071.293
Step-by-step explanation:
First year
$64,000
Second year
$64,000 + 8% of previous year
= $64,000 + 0.08*$64,000
= $69120
Third year
$69120 + 8% of previous year
= $69120 + 0.08*$69120
= $74649.6
Fourth year
$74649.6 + 8% of previous year
= $74649.6 + 0.08*$74649.6
= $80621.568
Fifth year
$80621.568 + 8% of previous year
= $80621.568 + 0.08*$80621.568
= $87071.293
Answer:
375.462.46
Step-by-step explanation:
Took the test and the other answer 87071.29 was wrong
What is the probability that the roll of a six-sided die will be either even or odd? A) 1 6 B) 1 4 C) 1 2 D) 1
Answer:
D) 1
Step-by-step explanation:
Every whole number (including the ones on a die) are either even or odd, nothing else. So it is guaranteed for the number to be even or odd.
Find the length of side a. Round to the nearest tenth.
A) 12
B) 378.4
C) 18.3
D) 19.5
Answer:
D) 19.5
Step-by-step explanation:
The law of cosines gives you the relation ...
a² = b² + c² - 2bc·cos(A)
Substituting the given values, you have ...
a² = 13² + 11² - 2·13·11·cos(108°) ≈ 378.379
a ≈ √378.379 ≈ 19.452 . . . . take the square root
a ≈ 19.5
The shapes of the horizontal cross-sections of the cone below are all congruent. True or false
Answer:
the answer is false
Step-by-step explanation:
False, The shapes of the horizontal cross-sections of the cone below are not all congruent.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We are given the statement,
'The shapes of the horizontal cross-sections of the cone are all congruent'.
Now, if we cut the cone horizontally, the cross-sectional shape is a 'circle'.
Further, the radius of the circle vary depending on the position form where the cone is cut i.e.
If cut from the top, the circle is approximately equal to a point.
If cut from the middle, the radius of the circle is less than the radius of the cone.
If cut from the bottom, the radius of the circle is equal to the radius of the cone.
Now, 'two figures are congruent if they overlap each other'.
Since, the circles have different radius, they will not overlap each other.
Thus, all the cross-sections of the cone would not be congruent.
Hence, the given statement is false.
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Identify the area of the figure. PLEASE HELP!!
Answer:
92m²
Step-by-step explanation:
The height of the triangle is the height of the square plus the height above the square, or 4+8=12 m.
The length of the hypotenuse is 15 m. The length of the known leg is 12 m.
Substitute 12 for b, 15 for c, and solve for a.
a=√15²-12²= √225−144 = √81 = 9
The bottom leg of the right triangle is 9 m.
To find the length of the base of the large triangle multiply the length of the bottom leg of the right triangle by 2.
The length of the base of the large triangle is (9)(2)=18 m.
Use a formula for the area of a triangle, A=12bh, to find the area of the triangle.
18 is base and 12 is height
A=(1/2)(18)(12)= 108
to find the area of the square:
A= 4²=16
A=108-16= 92m²
What is the simplest form of the expression below? 2x2 ? 10x ? 28 6x × 6 x ? 7
Final answer:
To simplify the expression, factorize the numerator and then cancel out any common terms with the denominator, resulting in the expression 1 / 3 + 2 / (3x).
Explanation:
To simplify the given expression 2x2 - 10x - 28 over 6x × (6x - 7), we need to factorize the numerator and see if any terms cancel out with the denominator. The factored form of the numerator is (2x + 4)(x - 7). The denominator can be written as 6x(6x - 7).
When we place the numerator over the denominator, we see that (x - 7) cancels out, simplifying our expression to (2x + 4) / 6x. This can further be simplified to 1 / 3 + 2 / (3x) by dividing both terms in the numerator by 6x
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.
2x − 7y = 4
3x + y = −17
A) 2(3x − 17) − 7y = 4
B) 2(−3x − 17) − 7y = 4
C) 2x − 7(3x − 17) = 4
D) 2x − 7(−3x − 17) = 4
Answer:
option D
2x − 7(−3x − 17) = 4
Step-by-step explanation:
Given in the question two equations
Equation 12x - 7y = 4
Equation 23x + y = -17
Rearranging equation 2 in terms of y
3x + y = -17
y = -17 - 3x
Put this value of y in Equation 1
2x - 7y = 4
2x - 7(-17 - 3x) = 4
So,
If you use the substitution method to solve the following system, new equation will be
2x - 7(- 3x - 17) = 4Answer:
The correct answer is D.
Step-by-step explanation:
I got it correct on the test. I hope this helps!
Explain the difference between an absolute minimum and a local minimum. a function f has an absolute minimum at x = c if f(c) is the smallest function value on the entire domain of f, whereas f has a local minimum at c if f(c) is the smallest function value when x is near
c.
Answer:
Step-by-step explanation:
Absolute minimum is where, in the infinite domain of f(x), the least value the function is the absolute minimum.
However, the local minimum is only a specific interval on the domain of f(x) where the lowest value is, but only in that interval.
So, usually, this comes up when you're dealing with 1st and 2nd derivatives. The first derivative tells you where local max and mins are, where the 2nd derivative tells you if the concavity is up or down.
An absolute minimum is the lowest point on the entire domain of a function, while a local minimum is the lowest point in a specific interval or neighborhood around a point on the graph.
Explanation:
An absolute minimum and a local minimum are both points on a graph where the function reaches its lowest value, but there are key differences between them.
An absolute minimum is the lowest point on the entire domain of the function. In other words, it is the smallest function value among all the points.
On the other hand, a local minimum is the lowest point in a specific interval or neighborhood around a particular point on the graph. It is possible for a function to have multiple local minima.
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PLEASE HELP!!!! WILL MARK BRAINLIEST!!!
A science museum has a spherical model of the earth with a diameter of 8.5 m. What is the volume of the
model? Use 3.14 for
and round your answer to the nearest whole number. Show your work.
Answer:
The volume of the model is [tex]321\ m^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere (model of the earth) is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
In this problem we have
[tex]r=8.5/2=4.25\ m[/tex] ----> the radius is half the diameter
substitute the values
[tex]V=\frac{4}{3}(3.14)(4.25)^{3}=321\ m^{3}[/tex]
How many 5-letter combinations can be created from the letters in the word "friendly"?
Answer:
1). infer 2). fired 3). filed 4). filer 5). elfin 6). nerdy 7). felid 8). finer 9). liner 10). lined 11). fiery 12). fiend 13). ferly 14). ferny 15). lindy 16). fined 17). lifer 18). field 19). redly 20). riley 21). riled 22). liney 23). rifle 24). drily 25). fried 26). diner 27). flier 28). flied 29). idler 30). deify 31). reify 32). yield 33). refly 34). dynel 35). edify 36). flyer
hope this helps :)
1. Solve for the variable in the following proportion.
n : 1/2 as 6 : 1 n=
2. Solve for the variable in the following proportion.
1/4 is to 1 1/4 as 2 is to b b=
3. In a group of students, the ratio of girls to boys is 3 to 2.
If there are 15 girls, how many total students are there?
A) 10
B) 20
C) 25
D) 30
4. On a field trip, there are 12 adults and 14 students.
What is the ratio of the number of adults to the total number of people on the field trip?
A) 6 to 13
B) 12 to 14
C) 26 to 12
D) 6 to 7
5. If 2d = 5c, then all of the following are true except _____.
A) 2/5= c/d
B) 5/2= d/c
C) 2/c= 5/d
D) 2/d= c/5
Please help and hurry. I need the answer as soon as possible.
The solutions to the given problems involve setting up and solving proportions, as well as understanding and applying ratios.
Explanation:1. To solve for the variable n in the proportion n : 1/2 as 6 : 1, we set up the equation n/0.5 = 6/1.
By cross-multiplying, we get n = 3.
2. To find the variable b in the proportion 1/4 is to 1 1/4 as 2 is to b, we write it as 1/4 : 5/4 = 2/b.
Cross-multiplying gives us b = 10.
3. To find out how many total students are there given the ratio of girls to boys is 3 to 2 and there are 15 girls, we use the ratio to find the number of boys 15 girls * (2 boys/3 girls) = 10 boys.
Adding the number of girls to the number of boys (15 + 10) gives us a total of 25 students, which is option (C).
4. For the field trip with 12 adults and 14 students, the ratio of the number of adults to the total number of people is 12/(12+14) = 12/26, which simplifies to 6/13, giving us option (A).
5. If 2d = 5c, the statement that is not true is D) 2/d = c/5, because when dividing both sides by the respective variables, it should be d/2 = c/5.
Final answer:
1. n = 3
2. b = 10
3. Option C: 25
4. Option A: 6 to 13
5. Option D: 2/d = c/5.
Explanation:
To solve for the variable n in the proportion n : 1/2 = 6 : 1,
you cross-multiply to get n * 1 = 6 * (1/2), which simplifies to n = 3.
Therefore, n=3.
To find the value of b in the proportion 1/4 : 1 1/4 = 2 : b,
we cross-multiply again, which gives us (1/4) * b = 2 * (5/4), after simplifying this, we get b = 10/1.
Therefore, b=10.
For the ratio of girls to boys, which is 3 to 2, if there are 15 girls, then for every 3 girls, there are 2 boys.
So, 15 girls represent 5 groups of 3 (because 15/3=5).
If there are 5 groups, then there must be 5 * 2 = 10 boys.
Therefore, adding the girls and boys gives us 15 + 10 = 25 total students, selecting Answer C) 25.
To determine the ratio of the number of adults to the total number of people on the field trip, we have 12 adults and 14 students, therefore the total number of people is 12 + 14 = 26.
The ratio of adults to the total number of people is 12:26, which simplifies to 6:13 after dividing both numbers by 2.
So, Answer A) 6 to 13 is correct.
If 2d = 5c, then dividing both sides by 2c gives us d/c = 5/2 or 2.5.
We can also divide by 2d to get c/d = 2/5.
The incorrect statement would be D) 2/d = c/5, as this doesn't match the original equation when cross-multiplied.
Can someone help me with this problem
Answer:
A = 20P = 6√10Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
A(-3, 0) , B(3, 2)
[tex]AB=\sqrt{(3-(-3))^2+(2-0)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}[/tex]
A(-3, 0), D(-2, -3)
[tex]AD=\sqrt{(-2-(-3))^2+(-3-0)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}[/tex]
AB = CD and AD = BC
The area of a rectangle:
[tex]A=(AB)(AD)[/tex]
Substitute:
[tex]A=(2\sqrt{10})(\sqrt{10})=(2)(10)=20[/tex]
The perimeter of a rectangle:
[tex]P=2(AB+AD)[/tex]
Substitute:
[tex]P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}[/tex]
(10CQ) Find the length of c
Answer:
The length of c = 18.7 units ⇒ answer (d)
Step-by-step explanation:
In triangle ABC:
∵ measure of angle B = 17° 55'
∵ measure of angle C = 98° 15'
∵ The sum of measures of the interior angles of a triangle is 180°
∴ The measure of angle A = 180 - (17° 55' + 98° 15') = 63° 50'
∵ The length of a = 17 units
* To find the length of c use the sin Rule
- a/sin(A) = b/sin(B) = c/sin(C)
- a is the side opposite to angle A, b is the side opposite
to angle B and c is the side opposite to angle C
∴ 17/sin(63° 50') = c/sin(98° 15')
* By using cross-multiplication
∴ c = (17 × sin(98° 15')) ÷ sin(63° 50')
∴ c = 18.7 units
∴ The length of c = 18.7 units ⇒ answer (d)
Which of the following is not an inequality?
A.) p ≥ 5
B.) m > 16
C.) 3y = 15
D.) k < 9
C.) 3y=15 is not an inequality.
An inequality compares the magnitude of two numbers (greater than, less than, etc.). Choice C uses an equals sign.
Hope this helps!!