how many modes are there in the following data set, which represents the number of days worked in october for 10 programmers of a software company? data set: 7,20,22,17,19,15,27,30,14,7
To mode of given data set of number of days worked in october for 10 programmers of a software company is 7 and 14.
The mode of a data set is the value that appears most frequently. In this case, we can see that both 7 and 14 appear twice, while all other values appear only once. Therefore, there are two modes in this data set: 7 and 14.
To solve mathematically, we can use the mode formula:
mode = value with the highest frequency
In this case, we have two values with the highest frequency, which are 7 and 14. Therefore, the mode of given data set is 7 and 14.
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For some value of b, the expression 3(5x - 1) + b(2x - 7) is a constant. What is the constant?
The value of the expression as a constant is 49.5
How to determine the constantFrom the question, we have the following parameters that can be used in our computation:
3(5x - 1) + b(2x - 7)
For the expression to be a constant, the following must be true
b(2x) = -3(5x)
Divide by x
b(2) = -3(5)
Divide by 2 and remove bracket
b = -7.5
Substitute the known values in the above equation, so, we have the following representation
3(5x - 1) -7.5(2x - 7)
So, we have
15x - 3 - 15x + 52.5
Evaluate the like terms
49.5
Hence, the constant is 49.5
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do 3 over 4 and 9 over 12 form a proportion
Answer:
0 over 12
Step-by-step explanation:
3/4 is equal to 9/12
so your basically taking 9/12 from 9/12
Find x
25
38
Please help me
Answer:
x ≈ 40.6
Step-by-step explanation:
using the sine ratio in the right triangle
sin38° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{25}{x}[/tex] ( multiply both sides by x )
x × sin38° = 25 ( divide both sides by sin38° )
x = [tex]\frac{25}{sin38}[/tex] ≈ 40.6 ( to 1 decimal place )
Answer:
x ≈ 40.6 units
(nearest tenth / one decimal place)
Step-by-step explanation:
You can use the law of sines in this situation since you know it is a right triangle because of the right angle, and you have an angle and a corresponding side.
Given this information, you can use the equation:
sin A / a = Sin B / b = Sin C / c
Given: A is 38°, a is 25, C is 90°.
Find: x which is side c
sin A / a = Sin B / b = Sin C / c →
[Substitute the information given]
Sin (38°) / 25 = Sin (90°) / c →
[Use the basic identity of sin(90°)]
Sin (38°) / 25 = 1 / c →
[Use the reciprocal rule]
25 / Sin(38°) = c →
[Rotate the equation]
c = 25 / Sin(38°) →
[Solve]
c = 40.606731137068..
[Reduce to the nearest tenth
(one decimal place) and set c to x]
x ≈ 40.6
There are 50 teachers in a school. 40% of them are women and the rest are men. If 70% of the women and 80% of the men are married, find the number of unmarried teachers in the school.
The sum of two numbers is 22. Two less than three times the smaller number is equal to the larger number x. Find the larger number.
y=6, x=16
you create a system with the two variables and manipulate an equation so that you can substitute in the other to make it a single-variable equation. you then solve for that variable by isolating it and you can solve for the second variable afterwards. hope this helps!
For each equation choose a value for x and then solve to find the corresponding y value that makes that equation true. Write your solutions in the form of an ordered pair (x,y).
1)6x=7y
2) 5x+3y=9
3) y+5-(1/3)x =7
The solutions are given in the ordered pairs.
What is an equation?An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.
We have to choose a value for x to find the corresponding y value to make the equation true.
1)6x=7y
To find x:
divide both sides by 6.
We get, [tex]\frac{6x}{6} =\frac{7y}{6}[/tex]⇒[tex]x=\frac{7y}{6}[/tex]
To find y:
divide both sides by 7.
We get, [tex]\frac{6x}{7} =\frac{7y}{7}[/tex] ⇒ [tex]y=\frac{6x}{7}[/tex]
Therefore solution for the given equation is [tex](\frac{7y}{6} ,\frac{6x}{7})[/tex]
2) 5x+3y=9
To find x:
subtract 3y from both sides,
⇒ 5x=9-3y then divide 5 on both sides,
⇒ [tex]\frac{5x}{5}=\frac{9-3y}{5}[/tex]⇒ [tex]x= \frac{9-3y}{5}[/tex]
To find y:
subtract 5x from both sides.
⇒3y=9-5x, then divide by 3 on both sides we get,
[tex]\frac{3y}{3}=\frac{9-5x}{3}[/tex]⇒[tex]y=\frac{-5x}{3}+3[/tex]
The solution for this equation is [tex](\frac{9-3y}{5},\frac{-5x}{3}+3)[/tex]
3) y+5-(1/3)x =7
To find x:
subtract y-5 from both sides we get,
[tex]-\frac{1}{3}x=2-y[/tex] then multiply both sides by -3,
[tex]\frac{\frac{-1}{3}x }{\frac{-1}{3}}=\frac{2-y}{\frac{-1}{3}}[/tex]⇒x=3y-6
To find y:
Subtract 5 from both sides.[tex]y-\frac{1}{3}x = 7-5[/tex] and add [tex]\frac{1}{3} x[/tex]
we get, [tex]y=2+\frac{1}{3}x[/tex]
The solution for this equation is ([tex](3y-6, 2+\frac{1}{3})[/tex]
Hence, the solutions are given in the ordered pairs.
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Determine the value of the missing angle using the inverse trig function.
Answer:
x = 59.036°
Step-by-step explanation:
tan (BÂC) = BC/AB
tan= opposite/ adjacent
Then subs AB = 3 BC= 5 BÂC= x into tan (BÂC) = BC/AB
tan(x)=5/3
x= tan^-1 (5/3)
x= 59.036°
B={z∣∣11≤z≤23andzis an even number }
I- uhm, it makes one but, I think that's just an equation...
Transcribed image text: Question 4 A certain automotive dealer sells only cars and trucks, and the ratio of cars to trucks on the lotis 11 to 33. If there are currently 51 trucks for sale, how many cars does the dealer have for sale! 34 68 136 272 thierronse
If the ratio of cars to trucks on the lot is 11 to 33 and there are currently 51 trucks for sale, then there are 17 cars for sale
The ratio of cars to truck on the lot = 11 : 33
Total number of trucks for sale = 51 truck
Consider the number of cars for sale = x
Then the ratios will be
11/33 = x / 51
Cross multiply the terms in the equation
33x = 51 × 11
33x = 561
Move 33 to the right hand side of the equation
x = 561 / 33
Divide the terms
x = 17
Therefore, the number of cars does the dealer have for sale is 17
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In the figure below, B is between A and C, and C is between B and D. If AD=13, BD=7, and BC=3, find AC.
AC =
The length of segment AC is equal to 9.
How to Find the Length of a Segment?Since B is between A and C, we can use the fact that AB + BC = AC. Similarly, since C is between B and D, we can use the fact to state the lengths of the following segments that: CD + BC = BD.
Substituting the given values, we get:
AB + BC = AC
CD + BC = BD
We are given segments BD = 7 and BC = 3, so we can substitute these values:
CD + 3 = 7
Solving for CD, we get:
CD = 7 - 3
CD = 4
Now we can use the fact that AD = AC + CD to solve for the length of segment AC:
AD = AC + CD
13 = AC + 4
AC = 9
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A set of eight cards were labeled with D, I, V, I, S, I, O, N. What is the sample space for choosing one card?
S = {V, S, I, D, I, I, N, O}
S = {D, I, S, O, N}
S = {V, I, O}
S = {D, I}
The sample space for choosing one card is S={V, S, I, D, I, I, N, O}.
What is a sample space?
A set of potential outcomes from a random experiment is known as a sample space. The sample space is identified by the letter "S". Events are a subset of the potential outcomes of an experiment. The results in a sample area could vary depending on the experiment.
Given that, a set of eight cards were labeled D, I, V, I, S, I, O, and N.
All the possible outcomes should be included in the sample space.
Here, the sample space will be { D, I, V, I,S, I, O, N}
Elements in the order will be
S={V, S, I, D, I, I, N, O}
Therefore, the sample space for the given set of cards is
S={V, S, I, D, I, I, N, O}.
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Need help with this question urgent please
Answer:
Step-by-step explanation:
First, add 7 to all parts of the inequality to isolate x.
-10+7 < 3x-7+7 ≤ 5+7
-3 < 3x ≤ 12
Then divide all sides by 3.
-1 < x ≤ 4
So x is greater than -1 but less than or equal to 4.
This can be written as (-1, 4] in interval notation.
Can someone help me find the point of intersection for:
2500(1. 25)^t=6000(0. 3)^t
algebraically? thank you.
The point of intersection can be found by setting the equations equal, dividing by the same quantity, taking the natural log, and dividing by ln(1.25).
[tex]2500(1.25^t) = 6000(0.3^t)[/tex]
[tex]2500*1.25^t = 6000*0.3^t[/tex]
Divide both sides by 2500:
[tex]1.25^t = 0.3^t * (6000/2500)[/tex]
Divide both sides by[tex]0.3^t[/tex]:
[tex]1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]
Take the natural log of both sides:
[tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]
Divide both sides by ln(1.25):
[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]
The point of intersection is t = ln((6000/2500) / [tex]0.3^t[/tex]) / ln(1.25).
The point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other and solving for the variable t. For example, if we want to find the point of intersection of [tex]2500(1.25^t) = 6000(0.3^t)[/tex], we can start by setting the two equations equal to each other and dividing both sides by [tex]2500: 1.25^t = 0.3^t * (6000/2500)[/tex]. Then we can divide both sides by[tex]0.3^t: 1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]. We then take the natural log of both sides: [tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]. Finally, we divide both sides by ln(1.25): [tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]. This means that the point of intersection is[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25).[/tex] In conclusion, the point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other, dividing both sides by the same quantity, taking the natural log of both sides, and then dividing both sides by ln(1.25).
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An altitude is drawn from the vertex of an isosceles triangle, forming a right angle
and two congruent triangles. As a result, the altitude cuts the base into two equal
segments. The length of the altitude is 11 inches, and the length of the base is 6
inches. Find the triangle's perimeter. Round to the nearest tenth of an inch.
8. the weights of cows offered at an auction in one region are normally distributed with a mean of 825.0 pounds and a standard deviation of 74.8 pounds. one cattleman only wants to bid on cows that are in the top 5% of weight. what is the lowest weight cow that the cattleman should bid on
The cattleman should bid on cows that weigh at least 944.0 pounds, which is the weight corresponding to the top 5% of the normally distributed weights of cows.
To determine the lowest weight cow that the cattleman should bid on, we need to find the weight that corresponds to the top 5% of the weight distribution.
Using the standard normal distribution, we can find the z-score that corresponds to the top 5% of the distribution as follows:
z = invNorm(0.95) ≈ 1.645
where invNorm is the inverse of the standard normal cumulative distribution function, which can be found using a statistical calculator or a standard normal distribution table.
Next, we can use the z-score formula to convert the z-score to a weight value:
z = (x - μ) / σ
Solving for x, we get:
x = z * σ + μ
Substituting the values given in the problem, we get:
x = 1.645 * 74.8 + 825.0
x ≈ 944.0 pounds
Therefore, the cattleman should bid on cows that weigh at least 944.0 pounds.
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a basketball player made 17 out of 20 free throws the practice. what percent of the free throws did the player miss?
Answer:
85%
Step-by-step explanation:
well, she missed 3 throws only from all 20's, hmmm if we take 20(origin amount) to be the 100%, what's 3 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 20 & 100\\ 3& x \end{array} \implies \cfrac{20}{3}~~=~~\cfrac{100}{x} \\\\\\ 20x=300\implies x=\cfrac{300}{20}\implies x=15[/tex]
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
The owner of two hotels is ordering towels. He bought 6 hand towels and 27 bath towels for his hotel in Campbell, spending a total of $255. He also ordered 50 hand towels and 27 bath towels for his hotel in Lowell, spending $343. How much does each towel cost?
A hand towel costs $ ----------, and a bath towel costs $ --------.
Answer:
A handtowel costs $2.00 and a bathtowel is $9.00
Step-by-step explanation:
Let h equal the cost of a handtowel. And let b equal the cost of a bathtowel.
In Campbell, they spent:
255 = 6h + 27b
In Lowell, they spent:
343 = 50h + 27b
Solve the system.
see image.
Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region between line y =3x -6 and line y=-2x+8 and
the x-axis with the help of integration will be 2.88 sq units.
What exactly is integration?
The process of computing an integral is known as integration. Mathematicians utilise integrals to compute a variety of useful quantities such as areas, volumes, displacement, and so on. When we talk about integrals, we usually imply definite integrals. Antiderivatives are represented by indefinite integrals. Integration, along with differentiation, is one of the two major calculus concepts in mathematics (which measure the rate of change of any function with respect to its variables).
Integral Fundamental
A definite integral is one that has both upper and lower bounds. For X to lie, only a true line may be utilised. The Definite Integral is also known as a Riemann Integral.
From a to b, use ∫f(x)dx
indefinite integral
Integrals are defined without upper and lower limits. It looks like this:
A indefinite Integral is written as:
∫f(x)dx = F(x) + C
Where C might be any constant and the function f(x) is referred to as the integrand.
Now,
As given in image
Area of the region will be =∫3x-6 dx from x=2 to 2.8 +∫-2x+8 from x=2.8 to 4.
=(3x²/2-6x) from x=2 to 2.8 + (-2x²/2+8x) from x=2.8 to 4.
=3*0.8*0.8/2-6*0.8-2*1.2*1.2+8*1.2
=2.88 sq units.
Hence,
The area of the region between line y =3x -6 and line y=-2x+8 and the x-axis with the help of integration will be 2.88 sq units.
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find the missing length
The value of the missing side of the given triangle would be = 12
How to calculate the value of the missing length?To calculate the value of the missing length the Pythagorean formula can be used such as;
c² = a² + b²
where;
C =?
a = 11
b = 5
C² = 11²+5²
= 121 + 25
= 146
C =√ 146
C = 12
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Convert 1000000 seconds to hrs, min and seconds
The value of the conversion is;
16, 666. 67 minutes
277.78 hours
What is conversion of units?Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.
From the information given, we have;
10⁶ seconds
But, we have to take note of;
60 seconds = 1 min
Then 10⁶ seconds = x min
cross multiply
x = 16, 666. 67 minutes
Also,
60 minutes = 1 hour
Then 16, 666. 67 minutes = x
cross multiply
x = 277.78 hours
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Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the critical value if the hypothesis is to be tested at the 0.05 level of significance?a. 1.28.b. 1.645.
c. 1.96.
d. 2.575.
The critical value if the hypothesis is to be tested at the 0.05 level of significance is 1.96 . So, option C is the correct answer.
To test the hypothesis that Woof Chow has a market share of 25%, we need to conduct a hypothesis test with the null hypothesis that the true proportion of dog owners who use Woof Chow is 0.25, and the alternative hypothesis that the true proportion is not 0.25.
Since the sample size n is large (n = 100), we can use the normal distribution to perform this test. The critical value for a two-tailed test at the 0.05 level of significance is given by:
z_critical = ±1.96
This value corresponds to the 2.5th and 97.5th percentiles of the standard normal distribution. The critical value is ±1.96 because we want to be 95% confident that the true proportion of dog owners who use Woof Chow is within a certain range, and the 95% confidence interval corresponds to two standard deviations from the mean.
To determine whether or not to reject the null hypothesis, we would calculate a test statistic (z-score) based on the sample proportion, and compare it to the critical value. If the test statistic falls outside the critical value, we would reject the null hypothesis and conclude that Woof Chow does not have a market share of 25%.
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Need help looking for the answer!!
Answer: it will take both the kids 5 hours
Step-by-step explanation: 45+5x5=50 5+9x5=5
9 times 5 is 45 in 5 hours Isaiah will have completed 5 pages and he started at 45 so in 5 hours Brenna will have completed 45 pages and she started at 5
Write a linear function for the data in the table.
X
y
0
8
1
4.5
2
1
3
-2.5
4
-6
18.85% of the pupils in Form 2 study craft, 72% study music and 60% study both subjects. What percentage study neither craft nor music?
Answer:
Step-by-step explanation:
Sorry cant help 18.85%
The length of a cell phone is 1.41.4 inches and the width is 3.83.8 inches. The company making the cell phone wants to make a new version whose length will be 0.910.91 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
A pet store has 6 cats. Here are their weights (in pounds).
13,9 ,9 ,15 ,12 , 16
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
Answer: About 50 lbs
Step-by-step explanation:
Answer:
12.3
Step-by-step explanation:
To find the mean you have to add all the numbers and divide by the number of numbers.
They add up to 74 and divided by the number of numbers(6)
you get 12.333...
Then yiu round up to 12.3
which equations for the measures of the unknown angles x and y are correct? check all that apply.(a) x=cos−1(a/c)x=cos−1(a/c)(b) x=sin−1(c/b)x=sin−1(c/b)(c) x=tan−1(c/a)x=tan−1(c/a)(d) y=sin−1(a/c)y=sin−1(a/c)(e)y=cos−1(c/b)y=cos−1(c/b)
The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Sin θ = Opposite Side to θ/Hypotenuse
Cos θ = Adjacent Side to θ/Hypotenuse
Tan θ = Opposite Side/Adjacent Side
Cot θ = Adjacent Side/Opposite Side
Sec θ = Hypotenuse/Adjacent Side
Cosec θ = Hypotenuse/Opposite Side
where, Hypotenuse (the longest side), Perpendicular (opposite side to the angle), Base (Adjacent side to the angle)
The inverse ratios start with the ratio and then find the angle that produces this ratio.
(a) x=cos−1(a/c)
(b) x=sin−1(c/b)
(c) x=tan−1(c/a)
(d) y=sin−1(a/c)
(e)y=cos−1(c/b)
The equations for the measures of the unknown angles x and y that are correct are (b), (c) and (e).
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What is another way to make 2.98?
Choose 1 answer:
B
1 one +8 tenths +18 hundredths
1 one 19 tenths 8 hundredths
1 one +10 tenths 8 hundredths
Answer:
Below
Step-by-step explanation:
1 + 19/10 + 8/100 = 1 + 1.9 + .08 = 2.98
What is the complete square corresponding to x2 – 6x? A. (x – 1.5)2 B. (x – 3)2 C. (x – 4.5)2 D. (x – 9)
Answer:
So the answer is C. (x - 3)^2.
Step-by-step explanation:
The complete square corresponding to x^2 - 6x is (x - 3)^2.
A complete square is a trinomial that can be written in the form (x - a)^2, where a is a constant. To find the complete square of x^2 - 6x, we need to rewrite x^2 - 6x into the form (x - a)^2. We do this by adding and subtracting a constant term to make the trinomial a perfect square.
x^2 - 6x + 9 = (x - 3)^2
So the answer is C. (x - 3)^2.
