We are asked to find the probability that a data value in a normal distribution is between a Z score of -1.52 and -0.34
[tex]P(-1.52First, we need to find out the probability corresponding to the given two Z-scoresFrom the Z-table, the probability corresponding to the Z-score -1.52 is 0.0643
From the Z-table, the probability corresponding to the Z-score -0.34 is 0.3669
So, the probability is
[tex]\begin{gathered} P(-1.52Therefore, the probability that a data value in a normal distribution is between a Z score of -1.52 and a Z score of -0.34 is 30.3%Option A is the correct answer.
I need help I am doing 8th grade conversion factors and there is only one way my teacher wants me to do it.
Conversion factors are the numbers for which we need to multiply a certain variable to convert it to another unit. In this case we need to convert gallons to cups, which have a conversion factor of 16 and minutes to seconds, which has a conversion rate of 60. Doing this we have:
[tex]\text{capacity = 24 gallons }\cdot\text{ 16 = }384\text{ cups}[/tex][tex]\text{time = 5 minutes }\cdot\text{ 60 = }300\text{ s}[/tex]The rate is:
[tex]\text{rate = }\frac{384}{300}\text{ = }1.28\text{ }\frac{cups}{s}[/tex]The sum of 3 and r is less than 7.What number sentence represents the statement?
The sum of 3 and r can be represented by "3 + r"
If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:
[tex]3+r<7[/tex]Find the missing number to make the fractions equivalent. 3/4 = 9/?
We have the following:
[tex]\frac{3}{4}=\frac{9}{x}[/tex]solving:
[tex]\begin{gathered} x=\frac{9\cdot4}{3} \\ x=12 \end{gathered}[/tex]Therefore, the answer is [B] 12
i am stuck and need help ASAP with itfind the area
Given:
Required:
We want to find the area of given
Explanation:
As we can see that measurement of given figure is 5 by 5 so it is square and the area of square is
[tex]5*5=25\text{ unit}^2[/tex]Final answer:
25 sq unit
how the position of the decimal point changes in a q u o t i e n t as you divide by Precinct power of 10.
When we divide a number by a power of 10, the decimal point changes its position. Specifically, the decimal points will move to the left according to the exponent of the power. For example, let's say we have the following division.
[tex]\frac{542}{10^3}[/tex]As we said before, we just have to move the decimal point to the left. In this case, we have to move it to 3 spots.
[tex]\frac{542}{10^3}=0.542[/tex]Hence, the division is equivalent to 0.542.
That's how the division works when you divide by a power of 10.
Simplify (5x + 7) - (x + 2)
You have the following expression:
(5x + 7) - (x + 2)
in order to simplify the previous expression, eliminate parenthesis and take into account that if a parenthesis is preceeded by a minus sign, when you elminate th eparenthesis the sign inside change to the opposite, just as follow:
(5x + 7) - (x + 2) =
5x + 7 - x - 2 =
5x - x + 7 - 2 =
4x + 5
Hence, the simplified expression is 4x + 5
two systems of equations are given below. for each system, choose the best description of its solution. if applicable, give the solution.
Let:
[tex]\begin{gathered} x-4y=8_{\text{ }}(1) \\ -x-4y=8_{\text{ }}(2) \\ \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (1)+(2) \\ x+(-x)+(-4y)+(-4y)=8+8 \\ -8y=16 \\ y=\frac{16}{-8} \\ y=-2 \end{gathered}[/tex]Replace the value of y into (1):
[tex]\begin{gathered} x-4(-2)=8 \\ x+8=8 \\ x=8-8 \\ x=0 \end{gathered}[/tex]The system has unique solution:
[tex](x,y)=(0,-2)[/tex]Select the correct answer. Which equation, when solved, gives 8 for the value of x? OA. +3 = =+14 OB. 5-9=31-12 OC. 21-2=r-4 OD. 5.-7=*=+14
Let's solve for each and see which gives 8
For A
5/2 x + 7/2 = 3/4 x + 14
collect like term aand solve for x
5/2 x - 3/4 x = 14 - 7/2
[tex]\frac{10x-3x}{4}=\frac{28-7}{2}[/tex][tex]\frac{7x}{4}=\frac{21}{2}[/tex][tex]x=\frac{21}{2}\times\frac{4}{7}=6[/tex]For B
5/4 x - 9 = 3/2 x -12
collect like term and solve for x
[tex]\frac{5}{4}x-\frac{3}{2}x=-12+9[/tex][tex]=\frac{5x-6x}{4}=-3[/tex][tex]-\frac{x}{4}=-3[/tex][tex]x=12[/tex]For C
5/4 x - 2 = 3/2 x - 4
collect like term and then solve for x
[tex]\frac{5}{4}x-\frac{3}{2}x=-4+2[/tex][tex]\frac{5x-6x}{4}=-2[/tex][tex]-\frac{x}{4}=-2[/tex][tex]x=8[/tex]For D
5/4 x - 7 = 3/4 x + 14
collect like term and solve for x
[tex]\frac{5}{4}x-\frac{3}{4}x=14+7[/tex][tex]\frac{2x}{4}=21[/tex][tex]x=42[/tex]Therefore, the correct option is C
write the equation of the polynomial with the following zeros in standard form
Answer:
x² - (5 + √7)x + 5√7
Explanation:
A polynomial with zeros at x = a and x = b can be written as:
(x - a)(x - b)
So, if the roots are x = √7 and x = 5, we can write the equation for the polynomial as follows:
(x - √7)(x - 5)
Then, to write it in standard form, we need to apply the distributive property, so:
[tex]\begin{gathered} (x-\sqrt[]{7})(x-5)=x\cdot x+x(-5)-\sqrt[]{7}x-\sqrt[]{7}(-5) \\ (x-\sqrt[]{7})(x-5)=x^2-5x-\sqrt[]{7}x+5\sqrt[]{7} \\ (x-\sqrt[]{7})(x-5)=x^2-(5+\sqrt[]{7})_{}x+5\sqrt[]{7} \end{gathered}[/tex]Therefore, the answer is:
x² - (5 + √7)x + 5√7
May I please get help with this math problem. I have been trying many times to find all correct answers to each length.
To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.
0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.
Procedure:
• Evaluating the first values given: (adding the two smallest values)
[tex]5.2+8.2=13.4[/tex]Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.
• Evaluating the second values given: (adding the two smallest values)
[tex]5+1=6[/tex]Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.
• Evaluating the third values given: (adding the two smallest values)
[tex]3+3=6[/tex]Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.
• Evaluating the final values given:
[tex]7+5=12[/tex]We can see that 12 < 13, so these cannot be side lengths of a triangle.
Answer:
• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.
,• 5, 10, 1: ,cannot be side lengths of a triangle.
,• 3, 3, 15: ,cannot be side lengths of a triangle.
,• 7, 13, 5: ,cannot be side lengths of a triangle.
10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work.
SOLUTION
A.
To solve this question, we will use the compound interest formula.
Which is:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ Since\text{ we are dealing with a yearly statistics, n = 1} \end{gathered}[/tex][tex]\begin{gathered} \text{From 1989 to 2007, there is a year difference of 18 years} \\ t=18 \\ A=109,185 \\ P=125,500 \\ We\text{ are looking for the continuous growth rate (r)} \\ \text{Now, we will substitute all these given parameters into the formula } \\ \text{above.} \end{gathered}[/tex][tex]\begin{gathered} 109,185=\text{ 125,500(1-}\frac{r}{100})^{18} \\ \frac{195185}{125500}=\frac{125500}{125500}(1-\frac{r}{100})^{18} \\ 0.87=(1-\frac{r}{100})^{18} \\ \text{take the natural logarithm of both sides:} \\ \ln 0.87=18\ln (1-\frac{r}{100}) \\ -0.1393=18\ln (1-\frac{r}{100}) \\ \frac{-0.1393}{18}=\ln (1-\frac{r}{100})_{}_{}_{}_{}_{} \\ -0.007737=\ln (1-\frac{r}{100}) \\ \end{gathered}[/tex][tex]\begin{gathered} e^{-0.007737}=(1-\frac{r}{100}) \\ 0.9922=1-\frac{r}{100} \\ \frac{r}{100}=1-0.9922 \\ \frac{r}{100}=0.007707 \\ r=100\times0.007707 \\ r=0.771\text{ \%} \end{gathered}[/tex]The continuous decay rate is 0.771%
B.
Using the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ t=2021-2007=14 \\ P=109,185 \\ n=1 \\ A=\text{?} \\ r=0.771 \\ \text{Substitute all the parameters into the formula above:} \end{gathered}[/tex][tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=109,185(1-\frac{0.771}{100})^{1\times14} \\ A=109,185\times0.89730607 \\ A=97,972.36 \\ A=97,972\text{ (to the nearest person)} \end{gathered}[/tex]The population of the city in the year 2021 is 97,972.
C.
We will use the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=97,890 \\ P=125,500 \\ r=0.771 \\ t=\text{?} \\ \text{Substitute all these parameters into the formula above:} \\ \end{gathered}[/tex][tex]\begin{gathered} 97890=125,500(1-\frac{0.771}{100})^t^{} \\ \frac{97890}{125500}=\frac{125500}{125500}(0.99229)^t \\ 0.78=0.99229^t \\ \ln 0.78=t\ln 0.99229 \\ -\frac{0.2485}{\ln 0.99229}=t \\ t=32.101 \\ SO\text{ the year that the population will reach 97,890 will be:} \\ 1989+32.101=2021.101 \\ \text{Which is approximately year 2021.} \end{gathered}[/tex]List all real values of x such that f(x) = 0, if there are no such real x, type DNE in the answer blank. If there is more than one real x, give a comma separated list (i.e: 1, 2) X =
Given the function defined as:
[tex]\begin{gathered} f(x)=-7+\frac{-8}{x-6} \\ \end{gathered}[/tex]The function can further be expressed as:
[tex]f(x)=-7-\frac{8}{x-6}[/tex]Find the LCM of the function;
[tex]\begin{gathered} f(x)=\frac{-7(x-6)-8}{x-6} \\ f(x)=\frac{-7x+42-8}{x-6} \\ f(x)=\frac{-7x+34}{x-6} \\ \end{gathered}[/tex]If f(x) = 0, then the value of x is calculated as:
[tex]\begin{gathered} \frac{-7x+34}{x-6}=0 \\ -7x+34=0 \\ -7x=0-34 \\ -7x=-34 \end{gathered}[/tex]Divide both sides of the equation by -7:
[tex]\begin{gathered} \frac{\cancel{-7}x}{\cancel{-7}}=\frac{\cancel{-}34}{\cancel{\square}7} \\ x=\frac{34}{7} \end{gathered}[/tex]Therefore the value of x if f(x) = 0 is 34/7
BUSINESS MATH calculate the state income tax owed on a 50,000 per year salary
Hello there. To solve this question, we have to remember some properties about income and taxes.
The following table shows the progressive tax rate for calculating individual income tax:
We want to calculate the state income tax owed on a $50,000 per year salary.
For this, notice this value is contained in the interval 17,001 and up, hence the progressive tax rate for this value is 5.75%.
In this case, the tax is simply given by the product between the value and the rate:
Don't forget to divide the percentage value by 100% before multiplying.
[tex]50000\cdot\dfrac{5.75}{100}=\$2,875[/tex]This is the state income tax owed by one whose salary is $50,000 per year.
Solve each word problem using a system of equations. Use substitution or elimination. 1. One number added to three times another number is 24. Five times the first number added to three times the other number is 36.
ANSWER
The first number is 3 and the second number is 7
EXPLANATION
Let the first number be x.
Let the second number be y.
The first line of the word problem is:
One number added to three times another number is 24.
This means that:
x + 3(y) = 24
=> x + 3y = 24 ______(1)
The second line of the word problem is:
Five times the first number added to three times the other number is 36.
5(x) + 3(y) = 36
5x + 3y = 36 ______(2)
Now, we have a system of equations:
x + 3y = 24 ____(1)
5x + 3y = 36 ___(2)
From the first equation, we have that:
x = 24 - 3y
Substitute that into the second equation:
5(24 - 3y) + 3y = 36
120 - 15y + 3y = 36
Collect like terms:
-15y + 3y = 36 - 120
-12y = -84
Divide through by -12:
y = -84 / -12
y = 7
Recall that:
x = 24 - 3y
=> x = 24 - 3(7) = 24 - 21
x = 3
Therefore, the first number is 3 and the second number is 7.
a is less than or equal to 10
The expression of the mathematical statement is a ≤ 10
How to represent the mathematical statement as an expression?From the question, we have the following mathematical statement that can be used in our computation:
a is less than or equal to 10
The key statement less than or equal to in mathematics and algebra can be represented using the following symbol
less than or equal to ⇒ ≤
So, we have the following representation
a is less than or equal to 10 ⇒ a is ≤ 10
This implies that we rewrite the above expression as follows
So, we have
a is less than or equal to 10 ⇒ a ≤ 10
The above expression cannot be further simplified
So, we leave it like that
Hence, the mathematical statement when expressed as an expression is a ≤ 10
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Kayla bought 2 1/2 yards of blue cloth for 6.97 and 1 1/2 yards of yellow cloth for half as much. She used 1/4 of the blue cloth to make her mother a apron. How much cloth did it take to make the apron
She used 1/4 of the blue cloth to make her mother a apron:
[tex]\frac{5}{2}\times\frac{1}{4}=\frac{5}{8}=0.625[/tex]She used 5/8 yd or 0.625yd of blue coth to make the apron
the probability he chooses orange fruit
Consider that the total number of fruits are 10. The probability to get some fruit is given by the quotient in between the number of suc a fruit and the total number of fruits.
Then, at the first time, the probability of getting a kiwi is:
p1 = 1/10 = 0.1 (becasue there is one kiwi)
After the kiwi is taken out, the number of fruits are 9. In this case, the probability of getting one orange is:
p2 = 3/9 = 0.33 (because there are three oranges)
THe probability of the two previous events, that is, to obtain one kwi and then one orange is the product of the probabilities p1 and p2:
P = p1*p2 = (0.1)(0.33) = 0.03
Hence, the probabilty is approximately 0.03
4. The relationship between temperature expressed in degrees Fahrenheit(F) and degrees Celsius (C) is given by the formula F= (9/5)C + 32. If the temperature is 5 degrees Fahrenheit, what is it in degrees Celsius ?
To calculate which value in Celsius the temperature of 5 Fº equates to, we first need to rewrite the expression isolating the "C" variable on the left side.
[tex]\begin{gathered} F=\frac{9}{5}\cdot C+32 \\ \frac{9}{5}\cdot C=F-32 \\ 9\cdot C=5\cdot F-160 \\ C=\frac{5}{9}\cdot F-\frac{160}{9} \\ \end{gathered}[/tex]We now need to replace F by 5.
[tex]\begin{gathered} C=\frac{5}{9}\cdot5-\frac{160}{9} \\ C=\frac{25}{9}-\frac{160}{9} \\ C=\frac{-135}{9} \\ C=-15 \end{gathered}[/tex]The temperature is -15 degrees in Celsius.
60% discount on $500 sweater
The discount price of the sweater will be, the original price minus the percentage of discount of the original price.
First, express the percentage of discount as a decimal:
60% = 60/100 = 0.6
so:
[tex]\begin{gathered} 500-0.6\cdot500 \\ 500-300=200 \end{gathered}[/tex]The discount price of the sweater is $200
Identify the postulate illustrated by the statement: Line ST connects pointS and point T
We have two points known to be ( S ) and ( T ). A line connects two points.
The minimum number of points that are required to form a straight line in a cartesian coordinate system are ( two ).
The minimum number of points that are required to form a plane in a cartesian coordinate system are ( three ) which will form two vectors i.e it requires two lines formed with a common point.
Two planes always intersect at exactly one point with direction normal to the two plane normal vectors.
Hence, the only possible postulate that relates two points is the formation of a line between two points; hence, the correct postulate for the given statement is:
[tex]\text{\textcolor{#FF7968}{Through any two points there is exactly one line}}[/tex]
Evaluate the expression 10 to the 2 power + (3 +5 to the power 2) -5
The answer is 159
The value of the expression 10 to the 2 power + (3 +5 to the power 2) -5 is 159.
What is an expression?An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The expression will be illustrated thus:
10² + (3 + 5)² - 5
= 100 + 8² - 5
= 100 + 64 - 5
= 164 - 5
= 159
The value is 159.
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simplifying with like terms; 2(m+10)
In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes
2 * m + 2 * 10
= 2m + 20
what are the two moves you can use to get the first figure to the second figure (dilation,rotation, reflection,and translation)
ANSWER:
Dilation and translation
EXPLANATION:
Looking at the figures, the two moves used to get the first figure to the second figure is dilation and translation.
The figure was translated 6 units right and 7 units down.
The translation rule that occured here is==> (x+6, y-7)
Also, a dilation with a scale factor of 2 occured here.
Therefore, a dilation and translation occured in order to get the first figure to the second figure.
I need to know The answer to this word problem
Given:
The little cheese 8 in $ 7.
The big cheese 10 in $ 9.
The cheese monster 12 in $ 12.
Required:
To find the ratio of little cheese, big cheese and cheese monster.
Explanation:
(1)
The crust to prize ratio for little cheese is,
[tex]\begin{gathered} 8:7=1:? \\ \\ =\frac{7}{8} \\ \\ =0.875 \end{gathered}[/tex](2)
The crust to prize ratio for big cheese is,
[tex]\begin{gathered} 10:9=1:? \\ \\ =\frac{9}{10} \\ \\ =0.9 \end{gathered}[/tex](3)
The crust to prize ratio for cheese monster cheese is,
[tex]\begin{gathered} 12:12=1:? \\ \\ =\frac{12}{12} \\ \\ =1 \end{gathered}[/tex](4)
The cheese monster is the best pizza for him.
Final Answer:
The crust to prize ratio for little cheese is = 0.875
The crust to prize ratio for big cheese is = 0.9
The crust to prize ratio for cheese monster cheese is = 1
The cheese monster is the best pizza for him.
What is a plane that is perpendicular to the base of a Cube and slices through the cube
The figure formed will be hexagonal
Graph the line with the given slope m and y-intercept b.
m = 1, b =0
Answer:
See graph
Step-by-step explanation:
Use the graph to find the horizontal asymptote of the rational function
Horizontal Asymptote
Observing the graph with the red dashed line, the horizontal asymptote of the function is at y = 6
Vertical asymptote
If we draw a line the graph we have the following
This indicates that the vertical asymptote is at x = 2.
8. In order to reach the top of a hill which is 250 feet high, one must travel 2000 feet straight up a road
which leads to the top. Find the number of degrees contained in the angle which the road makes with the
horizontal.
7.18° the angle which the road makes with the horizontal.
Define Trigonometric functions
The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given,
Height of hill = 250 feet
Length of the slope = 2000 feet
find the angle,
we know, sin(x) = perpendicular / hypotenuse
sin(x) = 250 / 2000
x = sin^-1 (0.125)
x = 7.18°
Hence, 7.18° the angle which the road makes with the horizontal.
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Caitlin and her family eat at at a restaurant. They spend $240 before tax. The restaurant charges them an additional 8% tax on their bill. Complete the two expressions that represent the total cost of the bill after the 8% tax is added to the bill. 240+ _______ x240240+_______Which 2 of these go in the blank?A.) 8B.) 0.08C.) 0.80D.) 19.20E.) 192F.) 259.20G.) 24
Answer:
B.) 0.08
D.) 19.20
Explanation:
The cost of the meal before tax = $240
Percentage added as tax = 8%
Therefore, the total cost of the bill after the 8% tax is added to the bill is:
[tex]\begin{gathered} 240+8\%\times240 \\ =240+\frac{8}{100}\times240 \\ =240+0.08\times240 \end{gathered}[/tex]If we simplify further, we have:
[tex]=240+19.20[/tex]sorry its blurry[tex] \frac{3x - 2}{4} = 2x - 8[/tex]
the given expression is,
[tex]\frac{3x-2}{4}=2x-8[/tex][tex]\begin{gathered} 3x-2=4(2x-8) \\ 3x-2=8x-32 \\ 8x-3x=32-2 \end{gathered}[/tex][tex]\begin{gathered} 5x=30 \\ x=\frac{30}{5} \\ x=6 \end{gathered}[/tex]thus, the answer is x = 6