Step-by-step explanation: If we use the variable p to represent our pizzas and s to represent our sodas, if our first equation states than 8 slices of pizza and 5 sodas cost $36.50, that's 8p + 5s = 3650.
Notice that I expressed cost in terms of cents so
that we can avoid having to deal with decimals.
In our second equation, 4 slices of pizza and
10 sodas cost $37, that's 4p + 10s = 3700.
Now let's rewrite our two equations on top of one another.
8p + 5s = 3650
4p + 10s = 3700
To solve this system of equations, I would use addition.
I would multiply the bottom equation by -2
to create a situation where our p's will cancel.
When we do that, we get -8p - 20s = -7400.
Now rewrite the equations once again ~
8p + 5s = 3650
-8p - 20s = -7400
Now add the equations together.
So we have -15s = -3,750.
Divide both sides by -15 and s = 250.
Remember that I expressed cost in terms of cents so
since s = 250, it really means that a soda is $2.50.
Now just plug an s back in for the s in one equation.
When we do this, we find that p = 300.
So a pizza is $3.00
A college currently has 600 students enrolled
full time. Of these students, 400 are science
majors while 200 are liberal arts majors. If
350 of the students are male, and 250 of the
males are science majors, how many female
students are liberal arts majors?
(A) 200
(B) 150
(C) 100
(D) 50
Answer:
C) 100
Step-by-step explanation:
250+600-350-400
850-350-400
500-400=100
What is the total repayment made, including principal and interest, on a loan of $1,100 at 3.5% interest compounded annually over four years?
The total repayment made, including principal and interest is $1262.27
Compound interestThe formula for calculating the compound interest is calculated as shown below;
A = P(1+r)^t
where
P is the principal = $1100
rate = 3.5% = 0.035
time "t" =4 years
Substitute
A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)
A = 1262.27
Hence the total repayment made, including principal and interest is $1262.27
learn more on compound interest here: https://brainly.com/question/24924853
#SPJ1
how much must be deposited today to have $45,000 in 5 years with a quarterly compounding and an APR of 7.3%
Answer:
$31,341.81
Step-by-step explanation:
The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years. We want to solve this for P:
A
------------------- = P
(1 + r/n)^(nt)
Substituting the given numerical values;
$45,000
--------------------------- = P
(1+0.073/4)^(4*5)
Using a calculator, we evaluate this expression, obtaining: $31,341.81
The speed of the boat in still water is mph.
The speed of a river current is 3 mph. If a boat travels 30 miles downstream in the same time that it takes to travel 20 miles upstream, find the speed of the boat in still water.
Answer: the speed of the stream is 9mph
PLEASE NEED HELP
The lifespans of crocodiles have an approximately Normal distribution, with a mean of 18 years and a standard deviation of 2.6 years. What proportion of crocodiles live between 17.5 and 20.5 years?
Find the z-table here.
0.3147
0.4068
0.5932
0.6853
Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 18, \sigma = 2.6[/tex]
The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:
X = 20.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20.5 - 18}{2.6}[/tex]
Z = 0.96
Z = 0.96 has a p-value of 0.8315.
X = 17.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 18}{2.6}[/tex]
Z = -0.19
Z = -0.19 has a p-value of 0.4247.
0.8315 - 0.4247 = 0.4068
0.4068 of crocodiles live between 17.5 and 20.5 years.
More can be learned about the normal distribution at https://brainly.com/question/4079902
#SPJ1
what is the value of x 44 inches and 55 inches triangle
Answer: I don't know what you are talking about, but if x is the area, then the answer is 1,210.
Step-by-step explanation: 44 x 55 x 1/2 = 1,210. The formula for the area of a triangle is 1/2 times length times height. Therefore, x = 1,210
Hope this helps.
4)48 Ans: The average height of a group of boys was 145 cm. When 2 boys joined the group, the average height became 148 cm. Given that the average height of the 2 additional boys was 160 cm, find the number of boys in the group at first.
Answer:
8
Step-by-step explanation:
The definition of an average can be used with the given values to write an equation for the number of boys.
SetupThe average is the total divided by the number. If there were n original boys, the total was T, where ...
T/n = 145 ⇒ T = 145n
Adding two boys with an average of 160 cm height, the new total became (T +2(160)) and the new average became ...
(T +2(160))/(n +2) = 148 ⇒ T = 148(n +2) -320
Equating the values of T, we have ...
T = 145n = 148(n +2) -320
SolutionSolving for n, we find ...
0 = 3n -24 . . . . . . . . . . . . subtract 145n and simplify
0 = n -8 . . . . . . . . . . . divide by 3
8 = n . . . . . . . . . . . add 8
The number of boys in the group at first was 8.
Find the measure of the ndicaited angle to the nearest degree 35 and 38
The measure of the indicated angle to the nearest degrees is 23 degrees.
How to find angle of a right angle triangle?The angle of a right angle triangle can be found as follows:
Therefore, the angle can be found using trigonometric ratios as follows;
cos ∅ = adjacent / hypotenuse
Therefore,
adjacent side = 35 units
hypotenuse side = 38 units
Hence,
cos ∅ = 35 / 38
∅ = cos⁻¹ 0.92105263157
∅ = 22.9272842944
∅ ≈ 23 degrees.
learn more on triangle here: brainly.com/question/20759265
#SPJ1
A group of people were asked if they had run a red light in the last year. 150 responded yes and 185 responded no. Find the probability that if a person is chosen at random, they have run a red light in the past year
The probability that a person chosen at random have run a red light in the past year is 0.45.
Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.
Probability lies between 0 and 1. The value of probability can be find by :
Probability= Number items/total items.
Number of people who said that they have run red light=150
Number of people who said that they have not run red light=185
Total people=150+185
=335 people
Probability that a person chosen at random have run red light in the past year=
=Number of people who said that they have run red lights / total people
=150/335
=0.447
After rounding off it will be 0.45.
Hence the probability that a person chosen at random have run a red light in the past year is 0.45.
Learn more about probability at https://brainly.com/question/24756209
#SPJ1
Find the equation of the line passing through the points (3,7) and (-2,5)
Answer:
The equation of the line passing through the points (3,7) and (-2,5) is y=⅖x+29/5
Step-by-step explanation:
Greetings !
[tex]first \: find \: the \: slope \: m \\ m = \frac{(Y₂-Y₁)}{(X₂-X₁)} ..substitute \: vlues \\ m = \frac{(5 - 7)}{( - 2 - 3)} = \frac{ - 2}{ - 5} = \frac{2}{5} \\ y = mx + b \: to \: find \: equation \: of \: aline \\ between \: two \: poins and \: use \: \\ one \: of \: the \: two \: points \: lets \: take( - 2.5) \\ y = mx + b \\ 5 = \frac{ - 2}{5} ( - 2) + b \\ 5 = \frac{ - 4}{5} + b \\ 5 + { - 4}^{5} = b \\ \frac{25 + 4}{5} = b \\ b = \frac{29}{5} \\ finally \: equation \: of \: the \: line \: will \: be \\ y = \frac{2}{5} x + \frac{29}{5} [/tex]
a circular garden has a diiameter of 6 yards what is the area of the garden use 3.14 for Tt
Given the diameter of the circular garden, the area of the garden is 28.36 yd².
What is the area of the garden?The area of a circle is expressed as; A = πr²
Given that;
Diameter d = 6ydRadius r = d/2 = 6yd/2 = 3ydArea A = ?A = πr²
A = 3.14 × (3yd)²
A = 3.14 × 9yd²
A = 28.36 yd²
Given the diameter of the circular garden, the area of the garden is 28.36 yd².
Learn more about circles here: brainly.com/question/11952845
#SPJ1
a store marks up the wholesale price of a skateboard by 112%. The retail price is $35. What is the wholesale price of the skateboard?
Please Help! Multiple Choice!
Using the z-distribution, the p-value would be given as follows:
b) 0.0086.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, it is tested if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex][tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex]Hence, for the distribution of differences, they are given by:
[tex]\overline{x} = 12 - 14 = -2[/tex].[tex]s = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{-2 - 0}{0.76}[/tex]
z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
Hence option B is correct.
More can be learned about the z-distribution at brainly.com/question/13873630
#SPJ1
I need answers please help me
Answer:
the ansqer is g(x) = 4^x-4 + 2
at a party 5/9 of the persons were men and the rest were women.if there was total 1260 persons find the number of women in the present
SOLUTION :
let total people in the party be x i.e. 1260
then , number of men = 5/9 of x
= 5/9 of 1260 = 5 × 140 = 700 men
now ,
number of women = Total person - (number of total men)
= ( 1260 - 700 ) women
= 560 women
________________________________
HOPE IT HELPS
MARK BRAINLIEST!
FOLLOW ME!
Simplify the following fractions.
Answer:
The solution for the above fraction is
[tex] \frac{146}{167} [/tex]
Step-by-step explanation:
Greetings!
look at the attachment above for the explanation.
(02.03 MC)
Choose the equation that represents the graph.
graph of a line passing through points negative 2 comma 0 and 0 comma negative 4
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
y = - 2x - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, - 4) ← 2 points on the line
m = [tex]\frac{-4-0}{0-(-2)}[/tex] = [tex]\frac{-4}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4
y = - 2x - 4 ← equation of line
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
x –3 –2 0 1 2
h(x) 0 –23 –12 0 0
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
h(x) = x3 + 6x2 + 11x – 6
h(x) = x3 – 7x + 6
h(x) = x3 – 7x – 6
h(x) = x4 + 2x3 – 7x2 – 8x + 12
The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
How to find the equation of a Polynomial?
From the given table, we see that the x-intercepts are;
(-3, 0), (1, 0) and (2, 0)
Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;
(x + 3), (x - 1), (x - 2)
Then, the polynomial will be;
h(x) = (x + 3) * (x - 1) * (x - 2)
h(x) = (x + 3)(x² - 3x + 2)
h(x) = x³ + 3x² - 3x² - 9x + 2x + 6
h(x) = x³ - 7x + 6
Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
Read more about Equation of Polynomial at; https://brainly.com/question/24348936
#SPJ1
Find the values of the variables in the parallelogram.
please help asap
tysm
Answer:
Step-by-step explanation:
Find two sets of parametric equations for the rectangular equation. y=(x-6)^2-7x.
If x=t+6 then y=
If x=7t then y=
Show all work !
The two sets of parametric equations for the rectangular equation are;
If x=t+6 then y= t²-7t-42.If x=7t then y= 49t² - 133t +36.What are the parametric equations from the rectangular equation?It follows from the task content that the parametric equations can be determined as follows;
By substituting the x= t+6 into the rectangular equation; we have;
y = (t+6-6)²-7(t+6)
y = t²-7t-42.
By substituting the x= 7t into the rectangular equation; we have;
y = (7t-6)² -7(7t)
y = 49t² - 84t +36 - 49t
y = 49t² - 133t +36.
Read more on parametric equations from rectangular equations;
https://brainly.com/question/23312942
#SPJ1
Company A manufactures and sells gidgets. The owners have determined that the company has the monthly revenue and cost functions shown, such that x represents the number of gidgets sold.
R(x) = 16x
C(x) = 12x + 1,424
At what number of gidgets sold will the company break-even (the point where revenue equals cost)?
Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.
What is the break-even point?The break-even point is the value of x for which:
R(x) = C(x).
In this problem, the functions are:
R(x) = 16x.C(x) = 12x + 1424.Hence:
R(x) = C(x)
16x = 12x + 1424
4x = 1424
x = 1424/4
x = 356
The company will break-even when 356 widgets are sold.
More can be learned about the break-even point of a company at https://brainly.com/question/9212451
#SPJ1
help!
Nora and Annie are raising money to purchase books for their school's library. The number of books they will be able to purchase for the library depends on the amount of money they raise.
b = the number of books Nora and Annie will be able to purchase
m = the amount of money Nora and Annie raise
Which of the variables is independent and which is dependent?
Answer: B is dependent and M is independent
Step-by-step explanation:
This is because the question says that they are raising money to buy books. In order to buy the books, they must raise money. So they raise money than buy the books which makes buying the books dependent on how much they raise.
Find the area of a triangle with base of 6m and height of 15m
Answer:
45 meters
Step-by-step explanation:
[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]
⊱________________________________________________________⊰
Answer:
A=45 m²
Step-by-step explanation:
The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].
where :
[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]
Substitute the values,
[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]
Done !! Hope this made sense to you :)
[tex]\small\boldsymbol{Calligraphy}[/tex]
⊱______________________________________________________⊰
Type the correct answer in each box. Use numerals instead of words.
Consider function g.
6,
0,
-4,
-8<-2
-2 ≤ x < 4
4 x < 10
What are the values of the function when = -2and when = 4?
g(x)
=
g (-2) =
g (4) =
Reset
Next
When x = -2, we use the second part of the function, so g(-2)=0.
Similarly, g(4) = -4.
Find the Diameter of the Circle with the following equation. Round to the nearest tenth.
(x - 2)2 + (y + 6)2 = 35
The diameter of the circle is 11.8 units
How to determine the diameter of the circle?The circle equation is given as:
(x - 2)^2 + (y + 6)^2 = 35
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where
Diameter = 2r
By comparing both equations, we have
r^2 = 35
Take the square root of both sides
r = 5.9
Multiply by 2
2r = 11.8
Hence, the diameter of the circle is 11.8 units
Read more about circle equation at:
https://brainly.com/question/10618691
#SPJ1
Emma throws an object upwards from a hill
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A non linear function is a function whose graph is not linear or can be represented by a straight line.
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
What is the value of z in the equation 4(2z + 3) = 12?
−13
12
0
12
Answer:
0
Step-by-step explanation:
8z +12 = 12
8z = 0
z =0
Answer:
The answer is 0
Step-by-step explanation:
4(2z+3)=12?=
We use the distributive property to distribute the 4 into the 2.
8z=3=12?=
8 + 3 is 12 so the z has no part to play in this.
z=0
You could also have divided from both sides of the equation, but doing it this way is easier for me.
HELP PLSSSSSSSSSSSS!!!!!
Answer:
6 x 2 x 2 x 1
Step-by-step explanation:
6 x 2 = 12
12 x 2 = 24
24 x 1 = 24
Solve for x if sqrt (3x-8) + 1 = sqrt (x+5)
The solution of x in the given expression [tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex] is 4. However, if it is [tex]\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}[/tex], it is 6.
What is the solution to algebraic expression?The solution to the given algebra expression involving surds can be seen in the steps below.
Given that:
[tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex]
Remove the square roots, we have:
12x - 32 = 4x² - 48x + 144
Solving the quadratic equation at the RHS and equating it to LHS, we have:
x = 11, x = 4
Verifying the solutions by replacing the value of x with the given equation:
x = 11 Falsex = 4 TrueTherefore, we can conclude that the value of x = 4
NOTE:
Given that:
[tex]\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}[/tex]
Square both sides
3x - 7 = x +5
Solve for x
3x - x = 5 + 7
2x = 12
x = 6
Learn more about solving to algebraic expressions here:
https://brainly.com/question/4344214
#SPJ1
copy the problems onto your paper, mark the given and prove the statements asked. if PO is congruent to PR and UO is congruent to UR prove angle O is congruent to angle R
The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.
What is the Side-side-side Congruence Theorem (SSS)?The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.
What is the CPCTC Theorem?The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.
We are asked to prove that ∠O ≅ ∠R.
With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).
We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.
This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.
Applying the CPCTC theorem, ∠O ≅ ∠R.
The two-column proof is attached in the image below.
Learn more about the Side-side-side Congruence Theorem (SSS) on:
https://brainly.com/question/4280133
#SPJ1