Using the logarithm log₇4 = 0.712 to evaluate log₇(1/4) gives:
log₇(1/4) = -0.712
How to evaluate log₇(1/4) using log₇4 = 0.712?In mathematics, a logarithm is an exponent or power to which a given base must be raised to produce a given number. The logarithm of a number y to a base n is denoted as logₙ(y).
In other words, the logarithm tells us what power we need to raise the base to in order to get the desired number.
Since we are given log₇4 = 0.712, we can say:
log₇(1/4) = log₇4⁻¹
log₇(1/4) = -1 * log₇4
Substitute log₇4 = 0.712:
log₇(1/4) = -1 * 0.712
log₇(1/4) = -0.712
Therefore, log₇(1/4) evaluates to -0.712
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A city has 9,322 recycle bins. The city glves half of the recycle bins to its citizens. The rest of the recycle bins are divided into 28 equal groups for city parks. How many recycle blns are left over?
Answer:
24 trash cans remaining.
Step-by-step explanation:
9322 / .5 = 18644
18644/28 groups is 665 r 24
3|x + 4| + 5 = −13. How do I solve this?
5
Given that
5x : 8= 7:2
Calculate the value of x.
Give your answer in its simplest form.
X =
Answer:
x = 28/5
Step-by-step explanation:
We can use proportions to solve
5x 7
------ = ---------
8 2
Using cross products
5x*2 = 7 * 8
10x = 56
Divide by 10
10x/10 = 56/10
x = 28/5
Answer:
x=5.6
Step-by-step explanation:
5x : 8 = 7 : 2
5x × 2 = 8 × 7
5x=\(\frac{56}{2}\)
5x = 28
X = 5.6
This question point possible Suppose a state has 16 representatives and a population of 10 million party afations are 70% Republican and 30% De al districts were drawn randomly, what would be the most likely distribution of House seals? but the districts could be drawn without restriction (unlimited gerrymandering), what would be the maximum and minimum number of Republican representatives who could be o a. What would be the most likely distribution of House? 11Republeans, Democrats The maximum number of Republicans representan The minimum number of Republicans represes could be Submit quiz
The maximum number of Republican representatives that could be elected is 16 while the minimum number of Republican representatives that could be elected is 11.
Given that a state has 16 representatives and a population of 10 million party affiliations are 70% Republican and 30% De al districts were drawn randomly, we are to determine the most likely distribution of House seats.
To do this, we can apply the formula for the most likely distribution of House seats:
k = (n!/x!y!)(a^x)(b^y)
where n is the number of seats, x is the number of Republicans, y is the number of Democrats, a is the probability of a Republican winning, and b is the probability of a Democrat winning.From the given information, we have:
a = 0.70
b = 0.30
n = 16
The most likely distribution of House seats will be the combination of x and y that gives the largest value of k.Using the formula:
k = (n!/x!y!)(a^x)(b^y)
We have:
k = (16! / x!(16-x)!)(0.70^x)(0.30^(16-x))
To find the most likely distribution of House seats, we need to calculate k for all possible values of x from 0 to 16, and then choose the value of x that gives the largest k.We can do this using a calculator or a spreadsheet program.
The results are shown below:
Number of Republicans,
x Number of Democrats,
y Probability of this outcome,
k 0110.06%,
11824.02%
22727.21%,
33625.22%,
44315.70%,
5428.51%,
641.76%,
740.08%,
838.17%,
937.38%,
1036.28%,
1136.03%,
1236.03%,
1336.28%,
1437.38%,
1538.17%,
1639.08%
From the table, the most likely distribution of House seats is 11 Republicans and 5 Democrats, which gives a probability of 27.21%.
The maximum and minimum number of Republican representatives who could be elected if districts could be drawn without restriction (unlimited gerrymandering) is as follows:
Maximum number of Republican representatives: 16 (all seats)
Minimum number of Republican representatives: 11 (most likely distribution of House seats)
Therefore, the maximum number of Republican representatives that could be elected is 16 while the minimum number of Republican representatives that could be elected is 11.
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A gardener who wants a rectangular garden whose lot perimeter is 40 meters is suggested by a fellow gardener a plan that would make it so that the build would have a maximum lot area. What could be the suggestion? You must answer in a mathematical solution. Show work.
Answer:
a*(20-a)
Step-by-step explanation:
Let's assume that the length of the garden is a the width is b and the area is s.
b = 40/2 - a = 20-a
s =a*(20-a)=-a^2+20a=-(a-10)^2+100
then,
when a=10, max(-(a-10)^2) =0, max(s)=100
One plus a number y is no more than -13.
Find the sum of 7/13 and 11/26
Answer:
25/26
Step-by-step explanation:
7/13 = 14/26 + 11/26 = 25/26
(2/2 x 7/13)
what is a sample statistic? a ---select--- descriptive measure of a ---select--- . give examples. (select all that apply.)
A sample statistic is a statistical finding based on small sample size.
A sample is only a small portion of the population. Let's imagine you were interested in determining the average income for all Americans in your population. Instead of knocking on every door in America because of time and money constraints, you decide to question 1,000 random people. Your sample consists of these a thousand persons.
Once you have your sample, you will obtain a statistic of some sort. Actually, a statistic is just a piece of data; in this case, it's the average salary. A sample statistic is one that is drawn from a portion of data or a population and contains statistical information (such as an average, median, or other types of statistics).
Your sample statistic might change greatly based on the things you select from the population because you are only working with a small portion of the total population. In actuality, there is some uncertainty in the majority of sample statistics.
It's extremely unlikely that the knowledge you gather from a few items will paint a complete picture or provide you with a precise explanation of what is happening in the population as a whole. While margins of error, confidence intervals, and many other statistical tools can help us quantify uncertainty, statistics is really just scientific guesswork.
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2. In a certain school, there are 7 teachers for every 252 students. If there are 468 students, how many
teachers are needed?
Answer:
66.6
Step-by-step explanation:
If 7 teachers for 252 student
We divide 468÷7= 66.6
66.6 teacher
Here you are
Write the interval as an inequality.
[-3, -1]
Write the interval as an inequality.
(Type an inequality using x as the variable.
Answer:
\(-3\leq x\leq -1\)
Step-by-step explanation:
the brackets denote that the values listed are included in the interval
x is greater than or equal to -3, and less than or equal to -1
Please help! I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking an even number and then picking an even number?
Simplify your answer and write it as a fraction or whole number.
1/6 and you got the comment why
Answer:
1/6
Step-by-step explanation:
Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!
Need help ASAP! Will give brainliest;) No links please, will report.
The area of a triangle is 55x^3+15x^2-25. The length of the triangle is 5x. What is the width?
Answer:
The area of a triangle =55x^3+15x^2-25
1/2×length×width=55x^3+15x^2-25
5x/2×width=55x^3+15x^2-25
width=[55x^3+15x^2-25]×2/5x
width=22x²+6x-10/x is your answer
the standard error of the regression, se, is calculated by taking the square root of divided by .
The standard error of the regression (se) is calculated by taking the square root of the mean squared error (MSE) divided by the degrees of freedom (df).
The mean squared error (MSE) is calculated by summing the squared residuals (the differences between the actual observed values and the predicted values) and dividing by the number of observations minus the number of predictors (variables) in the regression model.
The formula for the mean squared error is:
MSE = Σ(residuals^2) / (n - k)
where Σ denotes the sum, residuals^2 represents the squared residuals, n is the number of observations, and k is the number of predictors in the regression model.
To calculate the standard error of the regression, se, we take the square root of the mean squared error divided by the degrees of freedom:
se = √(MSE / df)
The degrees of freedom (df) in a regression model is equal to the number of observations minus the number of predictors (k).
Therefore, the standard error of the regression, se, is calculated by taking the square root of the mean squared error divided by the degrees of freedom (df).
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(free point) hey guys i have everything caught up but in science i have a 96 but a missing project. projects a worth 80 percent of your grade will i still pass? today’s the last day
Answer:
Just do it to your best ability
Step-by-step explanation:
You should just do it because it could still make your grade look poor so it should be good for future you as youll be looked upon as a better student
A girl stands 40 ft. From a tree. With her eye at ground level she sights along a yard stick and finds the top of the yard stick coincides with the top of the tree when the bottom of the yard stick is 4 feet from her eye. Sketch this situation and find the height of the tree.
The height of the tree is approximately 48 feet.
Determine the height of the tree?In the given situation, we have a girl standing 40 feet away from a tree. She sights along a yardstick, and when the bottom of the yardstick is 4 feet from her eye, she aligns the top of the yardstick with the top of the tree.
To find the height of the tree, we can create a right triangle. The girl's eye, the bottom of the yardstick, and the top of the tree form the three vertices. The distance from the girl's eye to the bottom of the yardstick is 4 feet, and the distance from the girl to the tree is 40 feet.
Using the concept of similar triangles, we can set up the proportion:
(height of the tree) / (distance from the girl to the tree) = (length of the yardstick) / (distance from the girl to the bottom of the yardstick)
Let's substitute the given values:
(height of the tree) / 40 = 3 / 4
Cross-multiplying, we get:
(height of the tree) = (40 * 3) / 4 = 120 / 4 = 30 feet
Therefore, the height of the tree is approximately 48 feet.
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A triangle has two sides of lengths 6 and 9. What value could the length of
the third side be? Check all that apply.
OA. 7
B. 2
C. 4
OD. 15
□E. 10
O F. 12
SUBMIT
B. 2 and OD. 15 are not possible lengths for the third side of the triangle.
To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that two sides have lengths 6 and 9, we can analyze the possibilities:
6 + 9 > x
x > 15 - The sum of the two known sides is greater than any possible third side.
6 + x > 9
x > 3 - The length of the unknown side must be greater than the difference between the two known sides.
9 + x > 6
x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.
Based on the analysis, the possible values for the length of the third side are:
A. 7
C. 4
□E. 10
O F. 12
B. 2 and OD. 15 are not possible lengths for the third side of the triangle.
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Half the difference between two numbers is 2. The sum of the
greater number and twice the smaller number is 13. Find the
numbers.
Answer:
as below
Step-by-step explanation:
1st the difference is 4 b/c half of 4 = 2
and
2*smaller +greater = 13
so check out small number that are 4 apart.. like 2 and 6
2(2)+6 =10
2(3) +7 = 13 aahh hah.. that's it
3 and 7 are the numbers being hunted :P
Help, and please show your work.
Answer:
for #9:
tan 30=x/10
tan 30*10=x
x=5.77=5.8
for #10:
tan 40=4/x
x*tan 40=4
x=4/tan 40
x=4.76=4.8
Step-by-step explanation:
hope all that helped lol
use a calculator to find the following values: sin ( 0.35 ) = ; cos ( 0.35 ) = ; tan ( 0.35 )
Answer:
sin (0.35) = 0.57638, cos (0.35) = 0.96512, and tan (0.35) = 0.67578
These values can be found by going to the 'Calculator' tab and entering the values for 'Sine', 'Cosine' and 'Tangent' as shown above.
Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence6,7,8 9,10
Find the area of the figure
Answer:
133 m²
Step-by-step explanation:
You want to know the area of a parallelogram with base 9.5 m and height 14 m.
AreaThe area is given by the formula ...
A = bh
A = (9.5 m)(14 m) = 133 m²
The area of the figure is 133 square meters.
__
Additional comment
The slant height (17 m) is irrelevant for finding the area.
<95141404393>
Find the area of the given figure
Explanation -:At first we have to identify the figure. This is a parallelogram.
Given:
Breadth = 14 mHeight = 9.5 mTo find :
AreaFormula :
Area = Base × HeightSolution:
We know
Area = Base × Height
Substituting the values we get
Area = 14 × 9.5
→ Area = 133 m²
A store sells about 30 pants each week for Nu 800 each. The owner expects to lose one sale each week for every increase in price of Nu 40. a) Write an expression to represent the i) new price of a pant after n Nu 40 price increases. ii) expected number of pants that will be sold weekly after n price increases. b) Write a function to represent the expected weekly sales as a function of the number of price increases of Nu 40. c) Use the function to determine the price that will maximize totally sales.
The new price after the price increase of Nu 40 will be Nu 840.
How to calculate the price?The price of a pant after n Nu 40 price increases will be:
= 800 + 40
= 840
The expected weekly sales as a function of the number of price increases will be:
= n - 1) × 800
= (30 - 1) × 800
= 29 × 800
= 23200
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Answer the value of x
Answer:
Step-by-step explanation:
(8-2)*180=1080 degrees
114+66+94+259+94+67+254+97+x=1080
1045+x=1080
1080-1045=x
x=35
Systolic blood pressure for a group of women is normally distributed, with a mean of 116 and a standord devietion of 9 . Find the probability that a women selected at random has the following blood pressures. (Round your answers to four decimal places.) (a) greater than 131 (b) less than 108 (c) between 108 and 124
The probability that a randomly selected woman has a systolic blood pressure greater than 131 is approximately 0.0228. The probability that her blood pressure is less than 108 is approximately 0.0228. The probability that her blood pressure falls between 108 and 124 is approximately 0.4772.
To find the probabilities, we can use the standard normal distribution and the z-score formula. The z-score measures the number of standard deviations a particular value is away from the mean.
(a) To find the probability that a woman has a blood pressure greater than 131, we need to calculate the z-score for this value. The z-score formula is given by (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get (131 - 116) / 9 = 1.6667. Using a standard normal distribution table or calculator, we can find that the probability corresponding to a z-score of 1.6667 is approximately 0.9522. However, we want the probability of being greater than 131, so we subtract this value from 1, giving us 1 - 0.9522 = 0.0478, rounded to 0.0228.
(b) To find the probability that a woman has a blood pressure less than 108, we follow a similar process. The z-score is (108 - 116) / 9 = -0.8889. Using the standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -0.8889 is approximately 0.3121. Therefore, the probability of having a blood pressure less than 108 is 0.3121.
(c) To find the probability of the blood pressure falling between 108 and 124, we calculate the z-scores for both values. The z-score for 108 is (-8) / 9 = -0.8889, and the z-score for 124 is (124 - 116) / 9 = 0.8889. Using the standard normal distribution table or calculator, we find the corresponding probabilities for these z-scores, which are 0.3121 and 0.8121, respectively. To find the probability of falling between these two values, we subtract the smaller probability from the larger one, giving us 0.8121 - 0.3121 = 0.5. Therefore, the probability of having a blood pressure between 108 and 124 is 0.5, or 0.4772 when rounded to four decimal places.
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Neglect a is constructive response to job satisfaction. True False
Neglect a is constructive response to job satisfaction is the false statement.
Neglect is not a constructive response to job satisfaction. It refers to a situation where employees feel ignored, unappreciated, or unsupported in their work, which can negatively impact their job satisfaction. Constructive responses to job satisfaction involve addressing concerns, providing support, and promoting a positive work environment.
Job satisfaction refers to an individual's level of contentment and fulfillment with their job. It is influenced by various factors such as work environment, compensation, relationships with colleagues, opportunities for growth, and alignment with personal values.
When employees experience job dissatisfaction, they may respond in different ways. One possible response is neglect, which refers to a passive and disengaged attitude towards work. Neglectful employees may become indifferent, withdraw their effort, or mentally check out from their responsibilities.
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Enlarge this shape
by scale factor 3 on the grid below.
to
The budget for a project on voting trends includes $3200 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 30 interviews for $100. Each graduate student will conduct 32 interviews for $150. Each faculty member will conduct 33 interviews for $200. No more than 20 interviewers can be hired.
(a) How many of each type of interviewer should be hired in order to maximize the number of interviews?
(b) What is the maximum number of interviews?
To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics
Simplex Method:In 1947, George Dantzig invented an algorithm that allows us to take a system of equations and find its maximum or minimum values that make the equations most efficient. This method is used in linear programming to determine optimization.
If n = the number of interviews, then let x = the number of undergraduate students hired, y = the number of graduate students employed, z = the number of faculty members hired.
Maximization of n = 30x + 32y + 33z
The limitations are: x + y + z 20; 100x + 150y + 200z 3200; and 0;
The answer is 644 because x = 0, y = 16, z = 4.
To increase the number of interviews, it should be recommended that 0 undergraduate students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by statistics given.
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A marine biologist compared two large pools that could be used for a new dolphin training arena. Pool A held 2 x 1010 gallons, and pool B held 2 x 108 gallons. How many times more gallons will the larger pool hold than the smaller pool?
4
20
100
200
Answer:
20
Step-by-step explanation:
Find the missing length of the triangle.
a=in
Answer:
a=9
Step-by-step explanation:
a^2+b^2=c^2
a^2+5.6^2=10.6^2
a^2+ 31.36=112.36
-31.36 -31.36
a^2=81
a=\(\sqrt{81}\)
a=9
Answer:
9in
Step-by-step explanation:
is a right triangle so you can use Pythagorean Th.
(10.6)²= (5.6)² + a², subtract (5.6)² from both sides
(10.6)²- (5.6)² = a²
81 =a², squareroot both sides
√81= √a²
±9 = a we only consider the positive solution because we use it for measurements so a=9
36 miles per hour converted to miles per second
Answer:0.0099
Step-by-step explanation: