1) The mean and the standard deviation of the total amount of money that she earns in a month are of:
Mean: 2650.Standard deviation: 211.9.2) The probability that she earns more than $2750 in a given month is of: 0.3192 = 31.92%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.When two variables are added, the mean is given by the sum of the means, hence:
[tex]\mu = 2100 + 550 = 2650[/tex]
The standard deviation is given by the square root of the sum of the variances, hence:
[tex]\sigma = \sqrt{200^2 + 70^2} = 211.9[/tex]
The probability that she earns more than $2750 in a given month is one subtracted by the p-value of Z = 2750, hence:
Z = (2750 - 2650)/211.9
Z = 0.47
Z = 0.47 has a p-value of 0.6808.
1 - 0.6808 = 0.3192 = 31.92%.
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19. The amount of money in a savings account increases from $ 250 to $ 270 in one month. If the percent increase is the same for every month, how much money will be in the account at the end of the next month?
(A) $ 291.60
(B) $ 295
(C) $ 289.60
(D) $ 300
Answer:
the answer will be the options A
{ (0,5), (9,2), (7,1), (6,3)}, What is the sum of all the elements in the range?
Answer:
11
Step-by-step explanation:
The range is the set of outputs, or the second element in each ordered pair.
The sum of these values is [tex]5+2+1+3=11[/tex].
how do i find x? please help me, I tried everything :(
pls help immediately
The simplified form of [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex] is [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, [tex]\sqrt{(2 - \sqrt5)^2} + \sqrt{(2 + \sqrt{5})^2}[/tex].
= [tex]\sqrt{4 - 4\sqrt{5} + 5}+ \sqrt{4 + 4\sqrt{5} + 5}[/tex].
= [tex]\sqrt{9 - 4\sqrt{5}} + \sqrt{9 + 4\sqrt{5}[/tex].
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b) The price of a house increases exponentially over time. A house presently costs $400,000, and it future
value can be modeled by the equation: A = 400,000 (1.04)*, where A is the value of the home after x years.
i) What percent is the house's value going up each year?
ii) What is the value of the home in 15 years?
ii) Assuming the trend continues, when will the value of the home double?
+4
Answer: The percent that the house's value is going up each year is given by the factor 1.04 - 1, which is 0.04. This represents a 4% increase in the value of the house each year.
ii) To find the value of the home in 15 years, you can substitute x = 15 into the equation to get:
A = 400,000 (1.04)^15
= 400,000 (1.7589)
= 700,356
Therefore, the value of the home in 15 years is $700,356.
iii) To find when the value of the home will double, you can set the value of A equal to 2*400,000 and solve for x:
2*400,000 = 400,000 (1.04)^x
2 = (1.04)^x
x = log(2)/log(1.04)
= 10.67
Therefore, it will take approximately 10.67 years for the value of the home to double, assuming the trend continues.
The local weather forecast has been accurate for 25 of the past 37 days. Based on this fact, what is the relative frequency probability that the
forecast for tomorrow will be accurate?
The relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.P(A) = Number of accurate days/ Total number of days
Here, the number of accurate days is 25 and total number of days is 37.
Substitute the above values as follows:
P(A) = 25/37
Hence, the relative frequency probability that the forecast for tomorrow will be accurate = 16/33.
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Solve.
9^(3x+1) = 27^2x
Answer: the equations has no solution
Step-by-step explanation:
[tex]9^{3x+1}=27^{2x}\\\\(3^2)^{3x+1}=(3^3)^{2x}\\\\3^{2(3x+1)}=3^{3(2x)}\\\\3^{6x+2}=3^{6x}\\\\Hence,\\\\6x+2=6x\\\\6x+2-6x=6x-6x\\\\2\neq 0\\\\Thus,\ the\ equations\ has\ no\ solution[/tex]
what is 2×1+2×
1/
10
+1×
1/
100
+3×
1/
1000
Answer:
2.213
2×1+2(1÷10)+1(1÷100)+3(1÷1000)
2×1+2×0.1+0.01+3×0.001
2+0.2+0.01+0.003
2.213 #
hope this will help ig
Answer:
2.213
Step-by-step explanation:
2×1+2(1÷10)+1(1÷100)+3(1÷1000)
2×1+2×0.1+0.01+3×0.001
2+0.2+0.01+0.003
2.213
In a recent international sport competition, the top three
countries--Country A, Country B, and Country C-won a total of
129 medals. Country B won 9 more medals than Country C.
Country A won 39 more medals than the total amount won by the
other two. How many medals did each of the top three countries
win?
The Medals are as follows:
A = 84 medalsB = 27 medalsC = 18 medalsWhat is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A + B + C = 119
Country B won 9 more than Country C so:
B = C + 9
Also, Country A won 39 more than the other two combined so:
A = B + C + 39
= (C + 9) + C + 39
= 2C + 48
Now we substitute into the equation:
A + B + C = 129
(2C + 48) + (C + 9) + C = 129
4C + 57 = 129
4C = 72
C = 18
So, if B = C + 9 then B = 27
and, A = 2C + 48 = 36+ 48 = 84
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An international company has 13,500 employees in one country. If this represents 19.6% of the company's employees, how many employees does it have in total?
Round your answer to the nearest whole number.
The required number of employees does it have in total is 68877.
What is percentage?A percentage is a part of an entire communicated as a number somewhere in the range of 0 and 100 as opposed to as a small portion. Something is all 100%, a big part of it is 50%, none of something is zero percent. To decide a rate, you partition the piece of the entire by the actual entire and duplicate by 100.
According to question:Let total population of the company be X
So,
19.6% of x = 13500
x(19.6/100) = 13500
X = 13500×100/19.6 = 68877 employees
Thus, required number of employees is 68877.
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A retirement account is opened with an initial deposit of $6,500 and earns 9.11% interest compounded monthly. What will the account be worth in 45 years?
Answer: $385,993.09
Step-by-step explanation:
Initial Amount: 6500
Rate: 0.0911 comp. monthly
Time: 45 years
Answer: 385,993.09
The four models each show two parallel lines cut by a transversal and some angle measures formed by the
intersection of the lines.
What are the values of angle measures a and b in model 4?
Move the correct answer to each box. Each answer may be used more than once. Not all answers will be used.
19° 71° 90° 109° 180° 119°
The value of a is _____, and the value of b is _____.
The value of a is 71°, and the value of b is 109°.
What is a parallel line?A parallel lines is defined as those type of line that are equidistant to each other which are on the same plane and they doesn't meet each other till infinity.
When two parallel lines are being intersected by another line called the transverse line, the following relationship is bound to occur such as;
Corresponding angles, Alternate Interior Angles, Alternate Interior Angles, Alternate Exterior Angles and Consecutive Interior Angles.From model 4, the pair of alternate exterior angles are equal in measure. That is 71° = angle opposite b°.
That is 180 - 71 = 109°
Also in model 4, the pair of alternate interior angles are equal in measure. a = 71°.
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An international company has 11,400 employees in one country if this represents 18.6% how many employees does it have in total?
Answer: about 61290 employees total
Step-by-step explanation:
18.6% is equal to 11400 employees in one country
18.6% of X = 11400
x=11400/0.186
x=61290
Note that the answer is rounded
The data set of the diameters of the metal cylinders manufactured an automatic machine has sample size of n = 25, mean of x = 49.98 mm and std. of S = 0.14 mm. Expected diameter of metal cylinder is mu = 50.00 mm. Can we be 95% confident that machine calibrated properly? {Solution Tips: Yes; if 95% confidence interval includes expected diameter of metal cylinder.}
95% confidence that machine calibrated properly is (48.536, 51.424).
We have given that,
n = 25
mean of x = 49.98 mm
S = 0.14 mm
μ = 50.00 mm
and CI = 95%
from t-table we know that,
t at 95% and n - 1 = 25 - 1 = 24 is 2.064
Therefore 95% of CI means that
(x - 2.064 × S√n, x + 2.064 × S√n)
(49.98 - 2.064 × 0.14√25, 49.98 + 2.064 × 0.14√25)
(49.98 - 2.064 × 0.7, 49.98 + 2.064 × 0.7)
(49.98 - 1.444 , 49.98 + 1.444)
(48.536, 51.424)
Therefore 95% confidence that machine calibrated properly is
(48.536, 51.424).
The 95% confidence interval is a range of values that you can be 95% confident contains the true mean of the population.
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The replacement set for an equation is {10, 24, 25, 36}.
The equation is represented by the sentence, "5/6 of a number is 30."
What is the solution set of the equation?
options:
Responses
{10}
{24}
{25}
{36}
ill give brainleist
{25} is the solution set of the equation {10, 24, 25, 36}.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given set of equation is {10, 24, 25, 36}
Since, The equation is represented by the sentence that is 5/6 of a number is 30.
So the required solution,
5/6 of the number 30 = 25
The solution set of the equation is {25}.
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one number is six less than a second number. Four times the first is 2 more than 6 times the second. Finde the numbers
The numbers are -19 and -13 by the given conditions.
How to solve word problems?
It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach. Aloud to yourself, read the issue.
Make a Drawing.Consider: "What am I trying to find?”List the items that have been provided.Locate the key phrases.Solve.Verify your work.Let the two numbers be x and y
One number is six less than a second number: x = y - 6 ⇒ i
Four times the first is 2 more than 6 times the second: 4x = 6y + 2 ⇒ ii
Substitute the value of x in (ii)
4(y-6) = 6y + 2
4y - 24 = 6y + 2
2y = -26
y = -13
Now substitute the value of y in (i);
x = -13 - 6
x = -19
Hence, the numbers are -19 and -13 by the given conditions.
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Which equation is equivalent to the given equation?
x² - 6x = 8
Answer:
(x-3)^2=17
Step-by-step explanation:
i took dis test b4
Will give brainliest!!!
What is the value of x?
Use the provided picture
Answer: C
Step-by-step explanation:
pythagorean theorem : a^2 + b^2 = c^2
8^2 + 8^2 = x^2
64 + 64 = x^2
128 = x^2
x = sqrt(128) square root both sides
x = 8sqrt(2) simplified
Answer: c, [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
Since this is a right triangle, we will use the Pythagorean theorem to help us solve for x.
Theorem:
a² + b² = c²
Substitue values:
8² + 8² = c²
To the power of 2:
64 + 64 = c²
Addition:
128 = c²
Square root both sides of the equation:
[tex]\sqrt{128}[/tex] = c
Reflexive property and breaking up 128 into two factors:
c = [tex]\sqrt{64*2}[/tex]
Square root of 64:
c = 8[tex]\sqrt{2}[/tex]
So, x = 8[tex]\sqrt{2}[/tex]
A 224-inch is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
A 60-inch piece is the shorter one. 180 inches long is the longer piece.
Step-by-step explanation:
Let's use the variables L and S to symbolise the longer and shorter pieces of pipe, respectively.Since the pipe will be the sum of L and S, we can create the following equation:L + S = 240
Additionally, we are aware that the longer piece is tri-times the shorter piece, which means:L = 3 S
Replace the first equation with the second equation:L + S = 240 ( 3 S ) + S = 240 \s 4 S = 240 \s S = 60
A 60-inch piece is the shorter one.Replace the following with the lengthier piece's length:L = 3 S L = 3 ( 60 )
L =180
180 inches long is the lengthier piece.Let's give the shorter piece a value.The length is "X." The other piece is three times as big, or three times.When you add them up, you get 4X.To learn more about the lengths of the pieces refer to:
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Find the sum
5. 1/4+ 1/28+ 1/70+ ,.....
The sum is 9/28
What is sum ?
The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million.
The end result of addition is a sum. For instance, the sum 10, written, is obtained by adding 1, 2, 3, and 4. (1) The sum of the numbers is known as the sum of the addends, or summands occasionally.
1/4 + 1/28 + 1/70 + 1/30 + ............ 1/700
Multiply and divide by 3 in whole series
⇒ 1/3 X [3/4 + 3/28 + 3/70 + 3/130 + ......... 3/700]
⇒1/3 X [1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+..........1/25-1/28]
⇒1/3 x [1 - 1/28]
⇒1/3 * 27/28
⇒ 9 / 28
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If a polynomial function has integer coefficients, then every rational zero of the function has the form p/q, where p is a factor of the ? and q is a factor of the ?
If a polynomial function has integer coefficients, the every rational zero of the function has the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
The rational zero theorem says that if a polynomial has integer coefficients then any rational zeros must be of the form p/q where p is the factor of the constant term and q is the factor pf the leading coefficients.
The rational zero theorem is used to determine the rational roots of a polynomial function.
Rational Zero Theorem statement:-
The rational zero theorem states that each rational zero(s) of a polynomial wit integer coefficients
f(x) = anxⁿ + an-1xⁿ⁻¹ + ... + a₂x² + a₁x + a₀ is of the form p/q where,
p is a factor of the constant a₀,
q is a factor of the leading coefficient an,
and p and q are relatively prime.
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6) Tyger and Newton have a long jump
competition. Tyger jumps 20% further than
Newton. If Newton jumps 475 cm, how far
does Tyger jump?
★need help solving this problem
help meeeeeeeeeee pleaseee
For an average intake of 2200 calories per day, the number of acres of land is approximately 2.
How to solve equations?If we are given all a function so in that case, we just need to substitute values given in question and solve for unknown variable that is to be determined.
C(x) is a variable that tells the number of calories consumed daily by a person
x is the number of acres that person own.
C(x) = 270㏑(x+1) +1900
In the given question number of acres ask a person to have who consumed 2200 calories in a day.
Therefore,
C(x)=2200
2200=270㏑(x+1) +1900
2200-1900=270㏑(x+1)
300=270㏑(x+1)
300/270 = ㏑(x+1)
10/9 = ㏑ (x+1)
x+1 = [tex]e^{\frac{10}{9} }[/tex]
x+1 = 3.037
x= 3.037-1
x=2.037
x=2(round off)
Therefore, 2 acres of land a person can consume 2200 calories in a day.
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Write answer using listing method
Using listing method the elements in the set are +2 and -2.
What is listing method ?
The listing approach involves writing the members of the set as a list, with commas separating the items and curly brackets enclosing the list. The rule or condition that may be used to determine if an object can belong to the set is specified when using the rule method for sets.
The members of a set are listed using this technique, with commas used to separate them and curly braces used to enclose the list. The four distinct seasons, for instance, can all be written as "Summer, Autumn, Spring, and Winter." The list's elements can be in any order, so don't worry.
We are given the set [tex]\left\{x \mid x^2=4\right\}[/tex]
all such x such that the perfect square is 4. Now, we have
[tex]$x^2=4 \Rightarrow x=\pm 2$[/tex]
Therefore, the elements in the set are +2 and -2.
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3) Juakali used Kingo's computer to type a report document which had 123 pages, and
each page occupied by 70 lines. 36 of 70 lines had 14 words while the remaining lines
had 18 words each. He wanted to take the document with him, and he had only a flash
disk with 256 KB as free space. Can he successfully save the document on the device?
Why?
To determine whether Juakali can successfully save the document on the flash disk, you can calculate the total number of words in the document and compare it to the amount of free space on the flash disk.
First, calculate the total number of lines in the document by multiplying the number of pages by the number of lines per page:
Total number of lines = 123 pages * 70 lines/page
= 8610 lines
Next, calculate the number of lines with 14 words by multiplying the total number of lines by the proportion of lines with 14 words:
Number of lines with 14 words = 8610 lines * 36/70
= 4380 lines
Calculate the total number of words in the lines with 14 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 14 words = 4380 lines * 14 words/line
= 61320 words
Calculate the number of lines with 18 words by subtracting the number of lines with 14 words from the total number of lines:
Number of lines with 18 words = 8610 lines - 4380 lines
= 4230 lines
Calculate the total number of words in the lines with 18 words by multiplying the number of lines by the number of words per line:
Total number of words in lines with 18 words = 4230 lines * 18 words/line
= 76140 words
Finally, add the total number of words in the lines with 14 words and the total number of words in the lines with 18 words to find the total number of words in the document:
Total number of words = 61320 words + 76140 words
= 137,460 words
To determine whether Juakali can successfully save the document on the flash disk, you can compare the total number of words in the document to the amount of free space on the flash disk. Since the flash disk has 256 KB of free space and there are 137,460 words in the document, Juakali will not be able to save the document on the flash disk. This is because the document is larger than the amount of free space available on the flash disk.
It is important to note that the capacity of a storage device is usually measured in bytes, and 1 KB is equal to 1024 bytes.
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Find the value of x.
The triangles are similar triangles. Then the value of the variable 'x' will be 6.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Similar triangles are shown below.
We know that the ratio of the corresponding sides of similar triangles remains constant. Then the equation is given as,
(6x - 1) / 15 = 14 / 6
Simplify the equation, then we have
(6x - 1) / 15 = 14 / 6
(6x - 1) / 5 = 7
6x - 1 = 35
6x = 36
x = 6
The triangles are comparable triangles. Then, at that point, the worth of the variable 'x' will be 6.
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A substance grows exponentially, and its weight doubles every 3 hours. Suppose it weighs 2 pounds at noon. After how many hours will it weigh 9 pounds? (Do not simplify result)
The substance will weigh 9 pounds after 4.5123 hours.
Here it is given that every 3 hours the weight of the substance doubles.
At 12 noon it weighed 2 pounds. Hence we will consider the initial weight to be 2.
Let the weight after x hours be w(x)
Here it doubles in 3 hours, hence the growth rate is 100%
Since the growth rate is given, the equation for the growth rate will be
w(x) = w₀.eˣ
where x = no. of 3-hour spans.
Here
w₀ = 2
and w(x) is given 9
Hence,
2eˣ = 9
or, e²ˣ = 9/2
Taking log on both sides we get
loge²ˣ = ln(9/2)
or, 2xloge = ln(9/2)
Since loge = 1 we get
2x = log(9/2)
or, x = 1.5041
Hence they will become 9 pounds after
3 X 1.5041 hours
= 4.5123 hours
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Which type of information could best be displayed on a two-way frequency table? Select all that apply.
A the number of library books, by genre, borrowed by children and adults during the summer
B the amount of rainfall each week during a year
c the number of daylight hours each day for a month
D the number and type of meals students choose in a lunchroom
Answer: B C and D
Step-by-step explanation:
Rewrite the following scientific notation numbers into standard form. (Be sure to use commas)
a. 3.23x10 -3
b. 7.45x10 5 =
Answer:
a. 0.00,323
b. 745,000
Step-by-step explanation:
a) move the decimal 3 places to the left
b) move the decimal 5 places to the right.
Given the function p(t) in the graph below, identify the intervals over which the function appears to be decreasing.
The interval of the domain where the function is decreasing are (0, 1) and (3, 4)
How to determine the increasing interval?From the question, we have the graph that represents the given parameters that can be used in our computation
To determine the decreasing interval on the graph, we look for the points where
As the values on the x-axis increaseThe values on the y-axis decreaseThe intervals that represent the above highlights are
From x = 0 to x = 1From x = 3 to x = 4This can be represented as (0, 1) and (3, 4)
Hence, the intervals are (0, 1) and (3, 4)
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