The z-score formula is given to be:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
[tex]\begin{gathered} x=score \\ \mu=mean \\ \sigma=standard\text{ }deviation \end{gathered}[/tex]From the question given, the mean and standard deviations are provided as:
[tex]\begin{gathered} \mu=1.07 \\ \sigma=0.12 \end{gathered}[/tex]Therefore, the z-score of exactly 1 gallon is calculated to be:
[tex]\begin{gathered} x=1 \\ \therefore \\ z=\frac{1-1.07}{0.12}=\frac{-0.07}{0.12} \\ z=-0.583 \end{gathered}[/tex]Therefore, the z-score is -0.583.
This tells us that a container with exactly one gallon of milk lies 0.583 standard deviations below the mean.
Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?
We have to find how far is the bird from Amanda.
With the information given, we can draw:
We can start by finding the third angle.
The sum of the angles have to be equal to 180°, so we can find it as:
[tex]\begin{gathered} \alpha+55\degree+63\degree=180\degree \\ \alpha=180-55-63 \\ \alpha=62\degree \end{gathered}[/tex]Now, we can apply the Law of Sines to find the distance between Amanda (A) and the bird (B):
[tex]\frac{AB}{\sin J}=\frac{AJ}{\sin B}[/tex]where AJ is the distance between Amanda and Jamie and AB is the distance between the bird and Amanda.
We then can solve for AB as:
[tex]\begin{gathered} AB=AJ\cdot\frac{\sin J}{\sin B} \\ AB=25\cdot\frac{\sin63\degree}{\sin62\degree} \\ AB\approx25\cdot\frac{0.891}{0.883} \\ AB\approx25.23 \end{gathered}[/tex]Answer: 25.23 [Option A]
Find the measure of Zx in the figure.
The measure of Zx isº.
57°
X
90°
...
Please help me with this
A sole trader operates his business from
a warehouse, which has been damaged
by a fire, which occurred at the end of
the financial year. After the fire, the
remaining inventory that is undamaged
amounts to GHC 2,000 (cost). The
accountant establishes the following
information: I Inventory at the
beginning of the year was GHC 16,000 II
Purchases during the year were GHC
115,000 III Sales during the year were
GHC 140,000 IV The trader sells his
goods at a mark-up of 25% of cost What
is the value of the inventory lost in fire?
Beginning inventory = 16,000 Purchase = 115,000 Sales = 140,000 Mark up = 25% on cost Undamanged inventory = 2,000
The value of the inventory lost in fire is 2,000
How do you take inventory loss due to fire into account?
The cost of products available for sale is then subtracted from the cost of goods sold. The quantity will reflect how much inventory the fire has actually destroyed. As an illustration, $275,000 minus $80,000 = $195,000, which represents the amount of inventory destroyed in the fire.
Calculate the quantity of inventory destroyed by deducting the cost of sold goods from the cost of goods that are still in stock. In this scenario, the amount of merchandise lost in the fire was $275,000 less $70,000, or $205,000.
To learn more about inventory loss refer to:
https://brainly.com/question/14159119
#SPJ13
Hello! By the way when answering the question just don’t mind my work shown or my answer I know for a fact I am wrong.
We have to calculate the height of the stack of hay bales.
We can start by calculating the volume as the number of bales times the volume of one hay:
[tex]\begin{gathered} V=n*V_0=8*(10+\frac{2}{3}) \\ V=8*10+8*\frac{2}{3} \\ V=80+\frac{16}{3} \\ V=80+\frac{15}{3}+\frac{1}{3} \\ V=80+5+\frac{1}{3} \\ V=85+\frac{1}{3} \end{gathered}[/tex]Now, we know that this volume will be the area of the base times the height.
The area of the base can be calculated as the product of the length and the width:
[tex]\begin{gathered} A_b=L*W \\ A_b=4*(1+\frac{1}{3}) \\ A_b=4+\frac{4}{3} \\ A_b=\frac{4*3+4}{3} \\ A_b=\frac{12+4}{3} \\ A_b=\frac{16}{3} \end{gathered}[/tex]We then can calculate the height as the volume divided by the base area:
[tex]\begin{gathered} h=\frac{V}{A} \\ h=\frac{85+\frac{1}{3}}{\frac{16}{3}} \\ h=\frac{85*3+1}{3}*\frac{3}{16} \\ h=\frac{256}{3}*\frac{3}{16} \\ h=\frac{256}{16} \\ h=16 \end{gathered}[/tex]Answer the height is 16 feet.
I need to know how to 53 evaluate the inverse trigonometric function give answers in both radians and degrees
GIVEN:
We are given the following trigonometric expression;
[tex]Tan^{-1}(-1)[/tex]Required;
We are required to evaluate and answer both in radians and in degrees.
Step-by-step solution;
We shall begin by using the trig property;
[tex]tan^{-1}(-x)=-tan^{-1}(x)[/tex]Therefore, we now have;
[tex]tan^{-1}(-1)=-tan^{-1}(1)[/tex]We now use the table of common values and we'll have;
[tex]tan^{-1}(1)=\frac{\pi}{4}[/tex]Therefore;
[tex]-tan^{-1}(1)=-\frac{\pi}{4}[/tex]We can now convert this to degrees;
[tex]\begin{gathered} Convert\text{ }radians\text{ }to\text{ }degrees: \\ \frac{r}{\pi}=\frac{d}{180} \end{gathered}[/tex]Substitute for r (radian measure):
[tex]\begin{gathered} \frac{-\frac{\pi}{4}}{\pi}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\div\frac{\pi}{1}=\frac{d}{180} \\ \\ -\frac{\pi}{4}\times\frac{1}{\pi}=\frac{d}{180} \\ \\ -\frac{1}{4}=\frac{d}{180} \end{gathered}[/tex]Now we can cross multiply;
[tex]\begin{gathered} -\frac{180}{4}=d \\ \\ -45=d \end{gathered}[/tex]Therefore,
ANSWER:
[tex]\begin{gathered} radians=-\frac{\pi}{4} \\ \\ degrees=-45\degree \end{gathered}[/tex]A portion of $ 100,000 (x) is invested with a 3% after one year. The rest of the investment (and) obtained a return of 1%. The total return on investment was $ 1,800. 1) What equation shows the return on investment? 2) What equation shows how the $ 100,000 was divided?3) how much money was invested at a 3% rate of return?4) how much money was invested at a rate of return of 1%
We can write a system of equations that describe our problem.
Since we don't know how the original $100,000 was divided, we call the two parts X and Y
So we know that X + Y = 100000
Then we know the Combined Interest coming from the accounts.
We use the Interest formula for return on investment:
I = P * r * t
were P is the principal, r is the percent rate (in decimal form), and t is the number of years (in our case 1)
Then the interest from the 3% account (let's call it I1) (if X amount of money was deposited there) is:
I1 = X * 0.03 * 1 = 0.03 X
Similarly, the interest I2 coming from the 1% account (if Y amount of money was deposited there) is given by:
I2 = Y * 0.01 * 1 = 0.01 Y
Then, the addition of these two interest is our total return of $1800:
0.03 X + 0.01 Y = 1800
Then our system of equations is:
X + Y = 100000
0.03 X + 0.01 Y = 1800
which we solve by substituting for example for Y in the first equation:
Y = 100000 - X
and replacing the Y by this expression in our second equation:
0.03 X + 0.01 (100000 - X) = 1800
use distributive property to eliminate parenthesis:
0.03 X + 1000 - 0.01 X = 1800
combine like terms
0.02 X + 1000 = 1800
subtract 1000 from both sides
0.02 X = 800
divide both sides by 0.02 to completely isolate X:
X = 800 / 0.02
X = $40000
This is the amount deposited on the 3% account
Then we easily calculate the amount deposited in the other account by replacing x with $40000 in the equation we use for substitution:
Y = $100000 - $40000 = $60000
Then, the amount deposited in the 1% account was $60000
and the amount deposited in the 3% account was $40000.
can you please help me? I'm having trouble with algebra 2 doing online school
Brianna, this is the solutiuon:
Part 2: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x - 1)² = (x - 1) * (x - 1)
x² - x - x + 1
x² - 2x + 1
Thus, b = -2. The correct answer is A.
Part 3: Recalling that the perfect square trinomial has the form:
ax² + bx + c
(x + 25)² = (x + 25) * (x + 25)
x² + 25x + 25x + 625
x² + 50x + 625
Therefore, c = 625. The correct answer is D.
Sophia is in the business of manufacturing phones. She must pay a daily fixed cost of $200 to rent the building and equipment, and also pays a cost of $100 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Answer:
C = 100p + 200
Step-by-step explanation:
Because C is the total cost per day, 200 is the y-intercept because it's paid daily. The 100 is the slope since "he pays a cost of $100 per phone produced
12. A high school principal wants to determine if students' mathematical reasoning ability has any impact on their membership in academic clubs at the school. Twenty students were selected and given a mathematical reasoning test, with scores ranging from o to 50 (higher scores indicate more mathematical reasoning ability). Students were motivated to do well on the test with a reward system. These same students' membership in academic clubs was verified. Identify the response variable. A. Mathematical reasoning ability B. The high school C. Mathematical reasoning test D. Membership in academic clubs
Response variable: The response variable is the subject of an experiment.
In this question:
The experiment is about the mathematical reasoning ability of the students whom are members of academic clubs. So, we are focusing on mathematical reasoning ability, which is the response variable.
The answer is option A
What is an equation of the points given? And is parallel to the line 4x-5y=5?
We know that two lines are parallel if they have the same slope. So we first find the slope of the given line. One way to do this is to rewrite the equation in its slope-intercept form, solving for y:
[tex]\begin{gathered} y=mx+b \\ \text{ Where} \\ m\text{ is the slope and} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=5 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=5-4x \\ -5y=5-4x \\ \text{ Divide by -5 from both sides} \\ \frac{-5y}{-5}=\frac{5-4x}{-5} \\ y=\frac{5}{-5}-\frac{4x}{-5} \\ y=-1+\frac{4x}{5} \\ y=\frac{4x}{5}-1 \\ y=\frac{4}{5}x-1 \end{gathered}[/tex]Now, we have the slope and a point through which the line passes:
[tex]\begin{gathered} m=\frac{4}{5} \\ (x_1,y_1)=(-5,2) \end{gathered}[/tex]Then, we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{4}{5}(x-(-5)_{}) \\ y-2=\frac{4}{5}(x+5_{}) \end{gathered}[/tex]The above equation is the equation of the line in its point-slope form. However, we can also rewrite the equation of the line in its standard form by solving for the constant:
[tex]ax+by=c\Rightarrow\text{ Standard form}[/tex][tex]\begin{gathered} y-2=\frac{4}{5}(x+5_{}) \\ \text{ Multiply by 5 from both sides of the equation} \\ 5(y-2)=5\cdot\frac{4}{5}(x+5_{}) \\ 5(y-2)=4(x+5_{}) \\ \text{ Apply the distributive property} \\ 5\cdot y-5\cdot2=4\cdot x+4\cdot5 \\ 5y-10=4x+20 \\ \text{ Subtract 5y from both sides} \\ 5y-10-5y=4x+20-5y \\ -10=4x+20-5y \\ \text{Subtract 20 from both sides } \\ -10-20=4x+20-5y-20 \\ -30=4x-5y \end{gathered}[/tex]Therefore, an equation of the line that passes through the point (-5,2) and is parallel to the line 4x - 5y = 5 is
[tex]\boldsymbol{4x-5y=-30}[/tex]How many different three-digit numbers can be written using digits from the set 5, 6, 7, 8, 9 without any repeating digits?A. 625B. 20C. 120D. 60
Given:
The given numbers are 5,6,7,8,9.
Required:
Find the way so three-digit numbers can be written using digits from the sets 5, 6, 7, 8, 9 without any repeating digits.
Explanation:
Let n is the total number then the way to write m digits number is given by the formula:
[tex]A(n,m)=\frac{n!}{(n-m)!}[/tex]So the way to write 3 digits numbers are:
[tex]\begin{gathered} A(5,3)=\frac{5!}{(5-3)!} \\ =\frac{5!}{2!} \\ =5\times4\times3 \\ =60 \end{gathered}[/tex]Final Answer:
Option D is the correct answer.
The cargo of the truck weighs at most 2,800 pounds. Use w to represent the weight (in pounds) of the cargo.To get the 10% discount, a shopper must spend no less than $100. Use d to represent the spending (in dollars) of a shopper who gets the discount
We can write this inequalities as:
If the cargo W has to be 2,800 pounds at most, then:
[tex]W\le2,800[/tex]The shopper has to spend $100 or more to get a discount, so the spending d to get a discount can be written as:
[tex]d\ge100[/tex]Find all the powers of four in the range of 4 and 1000
[tex] \sqrt{18} (523 \div 8)[/tex]help I need help
Solution
Given question
11.85 = 2.1n + 4.5
Requirement
To isolate n
Step 1
Using the subtraction property of equality to isolate the variable
11.85 - 4.5 = 2.1n + 4.5 -4.5
7.35 = 2.1n
Step 2
use the division property of equality to isolate the variable
7.35/2.1= 2.1n/2.1
n = 3.5
Answers are 1 first, then 2 next, those are the 2 steps
Find an equivalent fraction with the given denominator 7/8 = ?/72
To find the missing numerator si that both fractions are equivalent, you have to multiply both sides of the equal sign by 72:
[tex]\begin{gathered} 72\cdot\frac{7}{8}=72\cdot\frac{?}{72} \\ 63=\text{?} \end{gathered}[/tex]The missing numerator is 63
The equivalent fractions are:
[tex]\frac{7}{8}=\frac{63}{72}[/tex]12. Suppose you buy 20 gallons of gasoline in a city that collects excisetax of .16 per gallon. If you pay $1.25 per gallon, what percent of theprice is city excise tax?a.b.c.13.4%13.2%12.8%
We can calculate the percent of the price that is excise tax by dividing the amount of tax per gallon by the final price of the gallon.
If the tax is 0.16 per gallon and the final price is 1.25 per gallon, the percentage can be calculated as:
[tex]p=\frac{0.16}{1.25}\cdot100\text{ \%}=0.128\cdot100\text{ \%}=12.8\text{ \%}[/tex]The percentage that is city excise tax is 12.8% of the final price of the gasoline.
find the unit price of a six pack of water for $6.90 fill in the amount per bottle of water
Given:
six pack of water = $6.90
To find:
Unit(one) price of water bottle(Price of one water bottle).
[tex]\frac{6.90}{6}=1.15[/tex]Therefore,
The price of one water bottle is $1.15.
find the other binomial p squared -13 p +36 =(p-9)
To find the other factor of the polynomial
[tex]p^2-13p+36[/tex]We need to find two integers which multiplication gives 36 and addition is -13.
This integers would be -9 and -4, then we have
[tex]p^2-13p+36=p^2-9p-4p+36[/tex]now we factor the right term using common factors:
[tex]\begin{gathered} p^2-9p-4p+36=p(p-9)-4(p-9) \\ =(p-9)(p-4) \end{gathered}[/tex]Hence:
[tex]p^2-9p-4p=(p-9)(p-4)[/tex]Therefore, the other binomial we are looking for is (p-4).
Consider right triangle PQR what is the value of tan(R)
6/8
8/10
8/6
10/6
The value of tan(R) in the right triangle PQR where Perpendicular=QP, Base=RQ, Tan R=P/B. The slope of a straight line is the tangent of the angle made by the line with the positive x-axis.
What is perpendicular?Two geometric objects are perpendicular in simple geometry if they intersect at a right angle. The perpendicular symbol,⟂, can be used to graphically represent the condition of perpendicularity. It can be defined between two planes, two lines, or two planes and another line.
What is base?The base of a right angle triangle is the side on which it is positioned. The calculation can also be done using any of the two sides other than the hypotenuse as the base. It is the side of the right-angled triangle that is perpendicular to its base.
here,
Perpendicular=QP
Base=RQ
Tan R=P/B
=QP/RQ
Tan R=6/8
The perpendicular QP, base RQ, and tan's (R) values in the right triangle PQR. Tan's (R) = P/B. The tangent of the angle formed by the line with the positive x-axis is what determines a line's slope.
To know more about tan,
https://brainly.com/question/26719838?referrer=searchResults
#SPJ13
can I please get answer quickly I just need to confirm I got it right
SOLUTION
We want to find the magnitude of the vector (-3, 4)
Magnitude of a vector is given as
[tex]\begin{gathered} |v|=\sqrt{x^2+y^2} \\ (x,y)=(-3,4) \\ we\text{ have } \\ =\sqrt{(-3)^2+4^2} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{gathered}[/tex]Hence the answer is 5 units, the last option
Need to graph and then mark length of stay (in days) on the bottom of the graph. Need 4 points on graph and 4 number on bottom of graph
given the data
13,9,5,11,6,3,12,10,11,7,3,2,2,2,10,10,12,12,12,8,8
sort data
s= 2, 2, 2, 3, 3, 5, 6, 7, 8, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13
then we have
2 ---- 3
3 ----- 2
5----- 1
6 ---- 1
7 -----1
8------2
9 ------1
10-----3
11-------2
12------4
13-------1
Factoring the polynomial 12g + 20h
I'm not sure if you can exactly give me the answers, but I need help solving these types of questions, I will attach them below. they are about tangent lines.
Question 1
Explanation
To solve these types of questions, we will use the Tangent radius theorem
Tangent to a Circle Theorem
The tangent theorem states that a line is a tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
The figure below helps give a pictorial view
The principle to be used here for question 1 will be
[tex]x^2+8^2=17^2[/tex]Simplifying further
[tex]\begin{gathered} x^2+64=289 \\ x^2=289-64 \\ x^2=225 \\ x=\sqrt{225} \\ x=15 \end{gathered}[/tex]Thus, the value of x is 15 units
2. Jim is 8 years old, and his Uncle Bill is 512 times older than he his. What is his Uncle Bill's age?
Answer:
Uncle Bill has ignored the laws of nature and the known universe and reached a stunning 4096 years old
Step-by-step explanation:
Just multiply 8 * 512
500 * 8 = 4000, 12 * 8 = 96, 4000 + 96 = 4096
Answer:44
Step-by-step explanation:
How much would you need to deposit in an account now in order to have $20,000 in the account in 4 years? Assume the account earns 5% interest.I want answer and explanation.
The rule of the simple interest is
[tex]\begin{gathered} I=PRT \\ A=P+I \end{gathered}[/tex]I is the amount of interest
P is the initial amount
R is the interest rate in decimal
T is the time
We need to find the initial amount if the new amount is $20,000, the interest rate is 5% for 4 years, then
A = 20000
R = 5/100 = 0.05
T = 4
Substitute them in the rules above
[tex]\begin{gathered} I=P(0.05)(4) \\ I=0.2P \\ 20000=P+0.2P \\ 20000=1.2P \\ \frac{20000}{1.2}=\frac{1.2P}{1.2} \\ 16666.67=P \end{gathered}[/tex]You need to deposit $16,666.67
The rule of the compounded interest
[tex]A=P(1+r)^t[/tex]A is the new amount
P is the initial amount
r is the interest rate in decimal
t is the time
A = 20000
r = 0.05
t = 4
Substitute them in the rule above
[tex]\begin{gathered} 20000=P(1+0.05)^4 \\ 20000=P(1.05)^4 \\ \frac{20000}{(1.05)^4}=\frac{P(1.05)^4}{(1.05)^4} \\ 16454.05=P \end{gathered}[/tex]You need to deposit $16,454.05
5 6 7 8. One times a number equals 4 1
hello
to solve this problem, we need to find the property of equality
let the unknown number be represented by x
[tex]4=1\times x[/tex]to solve for x, divide both sides of the equation by 1
[tex]\begin{gathered} 4=1x \\ \frac{4}{1}=\frac{1x}{1} \\ x=4 \end{gathered}[/tex]the number here is 4
the property used to get the answer is division property of equality
a 14-member board used for admitted
Using the Borda's method, when one person is ranked as 1st, he/she gets 3 points, if he/she is ranked 2nd, get 2 points, also, if he/she is ranked as 3rd get 1 point, and finally, 0 points if she/he is ranked as 4th
so, let's detemine how many points got each one
Cardona: Was selected 1st by 6 people, 2nd by 2 people, 3rd by 4 people and 4th by 2 people
[tex]C=3*6+2*2+1*4=26[/tex]So, that's a total of 26 points
Pitts-Jones: Was selected as: #1 by 4 people, #2 by 3 people, #3 by 6 people and 4th by 1 person
[tex]P=3*4+2*3+1*6=24[/tex]So, that's 24 points for Pitts-Jones,
De Plata: Was ranked #1 by 2 people, #2 by 8 people, #3 by 1 person and #4 by 3 people
[tex]D=3*2+2*8+1*1=23[/tex]That's 23 points for De Plata
Vincent: Was ranked as #1 by 2 people, #2 by 1 person, #3 by 3 people and #4 by 8 people
[tex]V=3*2+2*1+1*3=11[/tex]that's 11 points for Vincent,
Answer: From the above, we can conclude that the winner using Borda's method is Cardona
A certain drug dosage calls for 330 mg per kg per day and is divided into four doses (1 every 6 hours). If a person weighs 210 pounds, how many milligrams of the drug should he receive every 6 hours?Round your answer to the nearest milligram. Do not include units with your answer.
First, we convert the 210 pounds to kilograms as the dose is given in mg per kg.
Recall that:
[tex]1pound=0.453592\text{ kilograms.}[/tex]Therefore:
[tex]210\text{ pounds=95.2544 kilograms.}[/tex]The dose call for 330 mg per kg, therefore, to get the dose for 95.2544 kg, we multiply by 95.2544:
[tex]330*95.2544\text{ mg=31433.952mg.}[/tex]Finally, dividing by 4 we get the dose the person should receive every 6 hours:
[tex]7858.488mg\approx7858mg.[/tex]Answer: [tex]7858.[/tex]1. Find all real solutions to each equation. (a) x(2x − 5) = 1
Use the distributive property to expand the parenthesis:
[tex]x(2x-5)=2x^2-5x[/tex]Then:
[tex]undefined[/tex]Hector is thirsty and opens up the refrigerator and finds a half full gallon of milk. Hector drinks 2/5 of the milk Later kevin opens up the refrigerator and finds some milk left in the gallon. He drinks 1/3 of what is left. Draw a picture of the situation above. Include the amount of milk before hector drank any, after hector drank some, and then after kevin drank some. What fraction is the entire gallon did kevin drink What fraction of the entire gallon is left after both hector and kevin drink some milk?
When Hector opens up the refrigerator he finds the next :
He drinks 2/5 of the milk he found, then he drank:
[tex]\frac{1}{2}\times\frac{2}{5}=\frac{1\times2}{2\times5}=\frac{2}{10}=\frac{1}{5}gallon[/tex]And he left in the bottle of milk:
[tex]\frac{1}{2}-\frac{1}{5}=\frac{5-2}{2\times5}=\frac{3}{10}gallons\text{ of milk}[/tex]And after that Kevin open up the refrigerator and finds the next:
Kevin drinks 1/3 of what is left, then he drinks:
[tex]\frac{3}{10}\times\frac{1}{3}=\frac{3\times1}{10\times3}=\frac{3}{30}=\frac{1}{10}\text{gallon of milk}[/tex]And then he left:
[tex]\frac{3}{10}-\frac{1}{10}=\frac{3-1}{10}=\frac{2}{10}=\frac{1}{5}[/tex]And the milk he left in the bottle is: