The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
We have been given that the terms of the series ∑n=1log 5r are in AP.
As per the given question,
∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)
n = 20
∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)
Using the property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))
∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)
∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)
Using property of logarithmic logₐ(xy) = logₐx + logₐy,
∑log(Sr)=20·1og(5)+log(1×2×3×...20)
∑log(5r) = 20-log(5)+log(201)
∑log(5r) = 32.365524703598
Rounded to the nearest hundredth decimal,
∑log(5r) = 32.37
Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.
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the data given to the right includes data from 37 candies, and 5 of them are red. the company that makes the candy claims 30% of its candies are red. use the sample data to construct a 95% confidence interval estimate of the percentage of red candies. what do you conclude about the claim of 30%?
The Sample proportion for the data to construct a 95% confidence interval is 0.1351.
The percentage of red candies is (24.5%, 2.52%)
What do you mean by sample proportion?
The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.
What is percentage?
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Sample proportion [tex]=\frac{5}{37}=0.1351[/tex]
For 95% confidence interval, z = 1.96
Hence,
95% confidence interval will be:
[tex]0.1351 \pm 1.96\times \sqrt{0.1351\times(1-0.1351)/37}[/tex]
[tex]0.1351\pm0.1099[/tex]
(0.245, 0.0252)
(24.5%, 2.52%)
Since the confidence interval only contains values less than 30%.
The result is not consistent with 34% rate reported by the candy maker.
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If the shared side between angles 1 and 2 has a measure of 2x+7 and the shared side between angles 3 and 4 has a measure of 7x+3, what is the value of X?
Round your answer to the nearest hundredth.
Answer:
x = 0.8Step-by-step explanation:
Both mentioned sides have equal length as opposite sides of a parallelogram.
Set equation and solve for x:
2x + 7 = 7x + 37x - 2x = 7 - 35x = 4x = 4/5x = 0.8A company has 35% and 3% hydrogen peroxide solutions. They need an 8 L container with a 12% concentration of hydrogen peroxide. How much of the 3% hydrogen peroxide solution should they include in the container?
Answer:
2 L
Step-by-step explanation:
If the first one is 12% then the 3% one would be 2L because of algebra
5.75 liters of 3 percent hydrogen peroxide solution are included by the company in the container.
What is the percentage?A measurement used to determine a number's value out of 100 is the percentage.
Hydrogen peroxide solutions in various containers have concentrations of 35% and 3%.
Since the corporation wants an 8-liter container with a 12% hydrogen peroxide concentration.
Use mixture and allegation property,
35 3
12
9 : 23
Total quantity = 23x + 9x = 32x
Since, the company wants 8 liters,
therefore, 32x = 8 ⇒ x = 1/4
3.5 percent hydrogen peroxide solution will be equal to = 23x = 23/4 = 5.75. 5.75 liters of 3 percent hydrogen peroxide solution are needed.
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What does the transformation f(x) → f(x + 3) - 7 do to the graph of f(x)? choose answer below:
translates it 7 units left and 3 units up
translates it 3 units left and 7 units up
translates it 7 units right and 3 units up
translates it 3 units left and 7 units down
Answer:
3 units left 7 units down
Step-by-step explanation:
if the sign is inside the bracket opposite sign
if the sign is outside the bracket leave it as it is
so (x+3)=0 which means x= -3 so 3 units left since it is on x axis. 7 is on y axis and since it is negative so 7 units down.
Which of the graphs below shows correctly plotted points for the following line? y=2x+3
Answer: The image is for an idea of what you should look for
Step-by-step explanation:
Select the correct answer. Maria donates a fixed amount, a, to a charity each month. If she donates $300 in 12 months, what is the equation for a? A. a + 300 = 12 B. a × 300 = 12 C. a × 12 = 300 D. a + 12 = 300 E. a + 32 = 100
Answer: C
she donates a for 12 months, the 12 in the a * 12=300. the a is the fixed amount, meaning she will donate a 12 times in a year.
Evaluate f(x)=3x-9, when x=-2
A. -18
B. -33
C. -3
D. -15
Answer:
d. -15
Step-by-step explanation:
f(x) = 3x - 9, when x = -2
Input -2 into the function for x and solve:
f(-2) = 3(-2) - 9
f(-2) = -15
Hope this helped :)
Using the declining-balance method, complete the table as shown (twice the straight-line rate): (Enter your answers as a whole dollar amount.)
Auto $29,000
5 years
Residual $2,000
Year Cost Accumulated
Depreciation B.O.Y Book Value B.O.Y Depreciation
Expense Accumulated
Depreciation E.O.Y Book Value E.O.Y
1 A B C D E F
2 G H I J K L
3 M N O P Q R
Using the double-declining-balance method of depreciation, the completion of the table as shown is as follows:
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
What is the double-declining-balance method?The double-declining-balance method is one of the depreciation methods in use, but it allocates more cost to the earlier years of the asset's life.
This depreciation method uses twice the straight-line rate, which is computed as the product of 100/estimated useful life multiplied by 2.
For each year's depreciation expense, the double rate is applied at the end of the year's balance.
For the last year, the difference between the previous year's ending balance and the residual value is taken as the depreciation expense.
Auto = $29,000
Estimated useful life = 5 years
Residual = $2,000
Depreciable amount = $27,000 ($29,000 - $2,000)
Straight-line depreciation rate = 20% (100/5)
Double-declining depreciation rate = 40% (20% x 2)
Depreciation Expense:1st year = $11,600 ($29,000 x 40%)
2nd year = $6,960 ($17,400 x 40%)
3rd year = $4,176 ($10,440 x 40%)
4th year = $2,506 ($6,264 x 40%)
5th year = $1,758 ($3,758 - $2,000)
Year Cost Accumulated Book Value Depreciation Accumulated Book
Depreciation B.O.Y Expense Depreciation Value
B.O.Y E.O.Y E.O.Y
1 $29,000 $0 $29,000 $11,600 $11,600 $17,400
2 $29,000 $11,600 $17,400 $6,960 $18,560 $10,440
3 $29,000 $18,560 $10,440 $4,176 $22,736 $6,264
4 $29,000 $22,736 $6,264 $2,506 $25,242 $3,758
5 $29,000 $25,242 $3,758 $1,758 $27,000 $2,000
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I need help! Theorem and Postulates! I will give brainliest....Please!
The theorem that proves that the triangles are congruent is the Hypotenuse-leg (HL) Congruence Theorem. The correct option is the first option - HL Congruence Theorem
Congruent triangles: Hypotenuse-leg theorem (HL)From the question, we are to determine by what theorem of postulate the triangles can be proven congruent.
From the Hypotenuse-leg theorem which states that "if the hypotenuse and a leg of a right triangle are each congruent with the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent".
From the given diagram, we can observe that the hypotenuse of the first triangle is congruent to the hypotenuse of the second triangle. Likewise, we can observe that one of the legs of the first triangle is congruent to the one of the legs of the other triangle.
Hence, the triangles are congruent by the Hypotenuse-leg theorem.
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PLEASE HELP ASAP 30 POINTS PLUS BRAINLEST Simplify (3.2 x 10^−9) − (6.4 x 10^−8). Write the final answer in scientific notation.
−6.08 x 10^−9
−6.08 x 10^−8
−3.2 x 10^−1
−3.2 x 10^1
Answer:
B. -6.08 x 10^-8
A certain disease has an incidence rate of 0.2%. If the false negative rate is 8% and the false positive rate is
1%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
According to the solving the probability will be 0.159.
What is probability?The area of mathematics known as probability deals with numerical assessments of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
In statistics, what exactly is a probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed in percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.
According to the given data:The incidence rate is = 0.2% or 0.002
The false negative rate is = 8% or 0.008
The false positive rate is = 1% or 0.001
The probability is
0.01*(1-0.002) + 0.95*0.002
= 0.00998 + 0.0019 = 0.01188
Probability that a person who tests positive actually has the disease would be represented as:
Let the probability be represented by = p
p * 0.01188 = 0.95 * 0.002
p = 0.0019/0.01188
p = 0.159
Hence, probability is 0.159
According to the solving the probability will be 0.159.
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Use the equation below to find p, if m = 5 and v = 23.
p = mv
The numerical value of p in the equation p = mv, when m = 5 and v = 23 is 115.
What is the value of p in the given equation?Given the equation in the question;
p = mvm = 5v = 23To determine the value of p, plug in the values of m and v and simplify.
p = mv
Plug in m = 5 and v = 23
p = 5 × 23
Multiply 5 and 23
p = 115
Therefore, the value of p is 115.
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Answer:
115
Step-by-step explanation:
m = 5
v = 23
p = mv
p = (5)(23)
p = 115
Write these as normal numbers.
b)
9.6 × 10⁹
Answer:
9600000000
Step-by-step explanation:
9.6 x (10^9)
First, write 10^9 as 1000000000
Multiply by 9.6
= 9600000000.
Compute ending work in process inventory for a manufacturer using the following information.
Rav materials purchased
Direct materials used
Direct labor used
Factory overhead
Work in process inventory, beginning
Cost of goods manufactured
Ending Work in Process Inventory is Computed as:
Work in process inventory, beginning
Total manufacturing costs
Total cost of work in process
Work in process inventory, ending
$ 133,200
82,600
61,000
103,400
26,800
234,000
Total cost of work in process Work in process inventory, ending=$1,320,000
What is computation?Any sort of arithmetic or non-arithmetic calculation that adheres to a well defined paradigm is referred to as computation.The scenario dictates that the computation of the provided data be as follows:-
Buying raw materials will cost $1,800,000.
$20k is the opening stock of raw materials.
Raw material closing stock: $3,140,000.
Purchase of raw materials plus opening stock of raw materials minus closing stock of raw materials equals direct material used.
= $1,800,000 + $20,000 - $3,140,000= $1,320,000learn more about computation here:
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a recipe requires 3/4 cup of water. Nora has a 1 1/2 cup measuring cup. how much of the measuring cup is filled with water?
Answer:
i think it is 15/20
Step-by-step explanation:
because 6/8,9/12,12/16
Write the number in two other forms (fraction, decimal, or percent) 355%
Answer:3.55 , 71/20
Step-by-step explanation:
Select the best answer for the question.
19. What is the sum of 1/9 2/3, and 5/18?
O A. 4/15
O B. 12/9
O C. 8/30
O D. 19/18
Answer:
the answer Is D 19/18
1/9 +2/3=1/9+ 6/9 =7/9
7/9 +5/18= 14/18 + 5/18 = 19/18
Solve for X in the equation;
2x+5=7
Answer:
x=1
Step-by-step explanation:
Answer: x=1
Step-by-step explanation:
2x + 5 = 7
2x + 5 - 5 = 7 - 5
2x = 2
2x/2 = 2/2
x=1
1. Assuming the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan. a. Calculate the total amount of loan, monthly rate, number of payment periods, monthly payment, total interest paid, and amount borrowed. b. With the aid of what PMT function in a one variable condition, calculate monthly payment, total amount payable, total interest payable for: 11 yrs, 14 yrs, 18 yrs ,20 yrs, 28 yrs, 31 yrs mortgage.
The total amount he will pay after 25 years is $18,97,500.
His monthly payment will be $6,325.
Given, the cost of mortgage is $720,000, and the owner of the house makes a down payment of $60,000, with 7.5% interest rate and 25 years repayment plan.
Now, the total amount of the loan be,
720000 - 60000 = 660,000
monthly rate = 7.5/12 = 0.625%
Number of payment periods = 25
Total amount he has to pay after 25 years,
660000 + (660000×7.5×25)/100
= $18,97,500
His monthly payment will be
1897500/25×12
= $6,325
Hence, the total amount he will pay after 25 years is $18,97,500
also, his monthly payment will be $6,325.
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A surveywas giben to people who awned a cerrain type of car what percent of the people surveyd were completely satisfief with the car?
Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.
A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes.
In this problem, researching in the internet, it is found that:
A total of 1260 + 650 + 180 = 2090 people were surveyed.
Of those, 1260 were completely satisfied.
Hence:
60.29% of the people surveyed were completely satisfied with the car.
Tonia hit 65% of the 20 pitches thrown to her at softball practice. Fill in the missing information and determine how many pitches Tonia hit.
Answer: 13
Step-by-step explanation:
20(.65) = 13
Hope that helps!
Select the correct answer from each drop-down menu. The general form of the equation of a circle is 7x2 + 7y2 − 28x + 42y − 35 = 0. The equation of this circle in standard form is . The center of the circle is at the point , and its radius is units.
[tex]7x^2+7y^2-28x+42y-35=0 \\ \\ x^2 +y^2-4x+6y-5=0 \\ \\ x^2+y^2-4x+6y=5 \\ \\ x^2-4x+4+y^2+6y+9=18 \\ \\ \boxed{(x-2)^2+(y+3)^2=18}[/tex]
So, the center is [tex](2,-3)[/tex] and the radius is [tex]3\sqrt{2}[/tex].
please find the difference 7(2x+4)-5x
Answer:
9x+28
Step-by-step explanation:
7(2x+4)_5x
14x+28-5x
9x+28
Fine the values of x and y.
Answer:
x = 55
y = 20
Step-by-step explanation:
Angles on a straight line sum to 180°.
Finding x
⇒ 75° + (2x - 5)° = 180°
⇒ 75 + 2x - 5 = 180
⇒ 2x + 70 = 180
⇒ 2x + 70 - 70 = 180 - 70
⇒ 2x = 110
⇒ 2x ÷ 2 = 110 ÷ 2
⇒ x = 55
Finding y
⇒ 75° + (4y + 25)° = 180°
⇒ 75 + 4y + 25 = 180
⇒ 4y + 100 = 180
⇒ 4y + 100 - 100 = 180 - 100
⇒ 4y = 80
⇒ 4y ÷ 4 = 80 ÷ 4
⇒ y = 20
Use the literal symbols listed at the end of the problem to translate the given statement into an algebraic formula.
In a given weight, the number of grams equals 454 times the number of pounds. (g. p)
Choose the correct formula below.
A. g=454 +p
C. p=454g
E. g=454-p
G. g= 454
——
p
B. p=454 +g
D. p=454-g
F. g=454p
H. g= p
—
454
(−3,y) and (x,2).
y=4x+6
orderd pair
The values of x and y are -1 and 6 respectively, this forms an ordered pair of (-3,6) and (-1,2).
What are the missing x and y values values of the given ordered pair?Given the equation and ordered pair in the question;
y = 4x + 6Point: (-3,y) Point; (x,2)Find the y-value by substituting the x-value into the equation and solving for y.
y = 4x + 6
Plug in x = -3
y = 4( -3 ) + 6
y = -12 + 6
y = 6
Find the x-value by substituting the y-value into the equation and solving for x.
y = 4x + 6
Plug in y = 2
2 = 4x + 6
2 - 6 = 4x
-4 = 4x
x = -4/4
x = -1
Therefore, the ordered pair are (-3,6) and (-1,2).
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The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than 4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 528 jawbreakers that weigh more than .4 ounces?
It would be unusual for this sample of 800 to contain 528 jawbreakers that weigh more than .4 ounces, using the binomial distribution, as 528 is more than 2.5 standard deviations above the mean.
What are unusual values in the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The mean of the binomial distribution is of:
E(X) = np.
The standard deviation of the binomial distribution is of:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The unusual measures are the ones that are more than 2.5 standard deviations from the mean.
The values of the parameters in this problem are given as follows:
p = 0.6, n = 800.
Hence the mean and the standard deviation are given as follows:
Mean: 800 x 0.6 = 480.Standard deviation: [tex]\sqrt{800 \times 0.6 \times 0.4} = 13.86[/tex]The upper bound of usual values is of:
480 + 2.5 x 13.86 = 514.65.
528 > 514.65, hence it is an unusual value.
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help please??? brainlest
4. Solve for y.
q
116° +15y - 4=180
After simplifying the expression, the value of y is 4.53.
In the given question,
We have to solve for y.
The given expression is 116° +15y - 4=180.
To solve for y we simplify the expression.
The expression is 116° +15y - 4=180
Now simplifying the expression.
Add 4 on both side
116° +15y - 4+4=180+4
116° +15y=184
Subtract 116 on both side
116° +15y-116°=184-116°
Simplifying
15y=184-116°
15y = 68
Divide by 15 on both side
15/15 y=68/15
y=4.53
Hence, the value of y is 4.53.
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One spring day, Harper noted the time of day and the temperature, in degrees
Fahrenheit. Her findings are as follows: At 6 a.m., the temperature was 58° F. For the
next 3 hours, the temperature rose 4° per hour. For the next 5 hours, it rose 1° per
hour. The temperature then stayed steady until 6 p.m. For the next 2 hours, the
temperature dropped 1° per hour. The temperature then dropped steadily until the
temperature was 70° at midnight. On the set of axes below, graph Harper's data.
The graph that shows Harper's data about temperature and time is shown below .
The graph is a relation that represents the relationship between two variables on the x and y axis .
In the question ,
Harper's data of time of day and the temperature, in degrees Fahrenheit is given,
the temperature at 6 a.m. = 58° F
for the next 3 hours the temperature rose 4° each hour means
in 3 hours it will rise 12°
So , the temperature at 9 a.m. = 70° F
For the next 5 hours, it rose 1° per hour which means
in 5 hours it will rise 5°
So , the temperature at 2 p.m. = 75° F
The temperature then stayed steady until 6 p.m. which means
temperature at 6 p.m. = 75° F
For the next 2 hours, the temperature dropped 1° per hour , which means
temperature at 8 p.m. = 73° F
the temperature at midnight = 70° F
So , from the above data the graph is shown below .
Therefore , The graph that shows Harper's data about temperature and time is shown below .
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