Answer:
1+2=5
Step-by-step explanation:
1+2=5
Help with the following equation 8x²-6x-5=x
Answer:
\(8 {x}^{2} - 6x - 5 = x\)
\(8 {x}^{2} - 7x - 5 = 0\)
x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)
= (7 + √(49 + 160))/16
= (7 + √209)/16
= -.4661, 1.3411 (to 4 decimal places)
Paul paid $663 for a new freezer. He paid for the freezer with his credit card, which has an interest rate of 15.28% compounded monthly, and made monthly payments for five years until the freezer was paid off. He kept the freezer for seven years, and it used an average of $2.14 of electricity per week. Paul made no other purchases or payments with his credit card until the freezer was paid off. Between the interest and the electricity, which component of the lifetime cost of the freezer was greater, and how much greater was it? (Round all dollar values to the nearest cent.)
a.
The interest cost $106.60 more than the electricity.
b.
The interest cost $173.24 more than the electricity.
c.
The electricity cost $489.76 more than the interest.
d.
The electricity cost $115.96 more than the interest.
Answer:
c
Step-by-step explanation:
The electricity cost $489.76 more than the interest.
Thus, option C is correct.
What is Interest cost?Interest cost is the total measure of interest a borrower pays on an obligation commitment over the existence of the getting. Interest is paid on the obligation notwithstanding reimbursement of head.
The formula will be:
I = A - P
I = 663(1 + 0.1528/12)^(5*12) - 663
I = 663(1 + 0.1528/12)^60- 663
I = 1416.51 - 663
I = $753.51
The bill for electricity for 7 years and 52 weeks per year will be
= 7 x 52 x 2.14
= $778.96
The electricity cost is bigger than the interest:
$778.96 is bigger than $753.51 by $25.45:
$778.96 - $753.51 = $25.45.
Therefore, option C is correct.
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A rectangle has a perimeter of 32 in. Find the length and width of the rectangle under which the area is the largest.
a. Let the width to be x and the length to be y , then the quantity to be maximized is (expressed as a function of both x and y) A=_____
b. The condition that x and y must satisfy is y=______
Answer:
Length of the rectangle is 8 in and the breadth is 8 in.
a. \(A=xy\)
b. \(y=16-x\)
Step-by-step explanation:
Length = x
Breadth = y
Area is given by \(A=xy\)
Perimeter of rectangle is given by
\(2(x+y)=32\\\Rightarrow x+y=16\\\Rightarrow y=16-x\)
The condition that x and must satisfy is \(y=16-x\)
So, area is
\(A(x)=x(16-x)\\\Rightarrow A(x)=16x-x^2\)
Differentiating with respect to x we get
\(A'(x)=16-2x\)
Equating with zero
\(0=16-2x\\\Rightarrow x=\dfrac{16}{2}\\\Rightarrow x=8\)
Double derivative of A(x)
\(A''(x)=-2\)
So \(A''(x)<0\) which means \(A(x)\) is maximum at \(x = 8\)
\(y=16-x=16-8\\\Rightarrow y=8\)
So length of the rectangle is 8 in and the breadth is 8 in.
Match each expression with A, B, C or D.
A=a^3
B=6a
C=12a
D=3a^2
i)3a x 4
ii)a^2xa
iii) 6 1/2 a^2
The matching expressions are:
\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)
i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.
ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.
iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.
To understand the matching expressions, let's break down each one:
i) 3a x 4:
This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).
ii) a^2 x a:
This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).
iii) 6 × 1/2 a^2:
This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).
Therefore, the matching expressions are:
i) 3a x 4 = C (12a)
ii) a^2 x a = A (a^3)
iii) 6 × 1/2 a^2 = D (3a^2)
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Suppose there is a 1.2 Fahrenheit drop in temperature for every thousand feet that an airplane climbs into the sky if the temperature on the ground is 64.7 Fahrenheit what will the temperature be when the plane reaches an altitude of 5000 feet
9514 1404 393
Answer:
58.7 °F
Step-by-step explanation:
At 5000 feet, the airplane is 5 times 1000 feet above the ground, so the temperature will have dropped 5 times 1.2 °F.
64.7 - 5×1.2 = 64.7 -6.0 = 58.7
At 5000 feet, the temperature is 58.7 °F.
Julia went to the store to buy some cherries. The price per pound of the cherries is $7.50 per pound and she has a coupon for $3.50 off the final amount. With the coupon, how much would Julia have to pay to buy 2 pounds of cherries? Also, write an expression for the cost to buy pp pounds of cherries, assuming at least one pound is purchased
Julia have to pay to buy 2 pounds of cherries is $11.50. The cost to buy p pounds of cherries is 7.50p.
To find price of 2 pound of cherries we have to calculate:
The price per pound pound of cherries = $7.50
The price of 2 pound of cherries = $15.00
when the coupon value of $3.50 has been deducted from purchase cost then the final price
= $15.00 - $3.50
= $11.50.
cost of p pounds of cherries=(p x $7.5)
cost of p pounds of cherries=7.50p
Julia have to pay to buy 2 pounds of cherries is $11.50. The cost to buy p pounds of cherries is 7.50p.
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A
B
C
D
Pick a letter
Answer: D
Step-by-step explanation:
1 in.=1488 milesx5=7440 miles.
Area= pi x r^2
=pi x (7440)^2 or option D.
Hope this helps :)
PLEASE HELP 15 POINTS ON THE LINE SO PLEASE HELP Dylan’s dad purchased a car from his uncle and plans to give it to Dylan for his 16th birthday. His dad only paid $245.40 which is 30% of the original cost. How much was Dylan’s uncle selling the car for originally?
Answer:
$7,362
Step-by-step explanation:
its easy multiplication
$245.40 x 30
Answer:
818
Step-by-step explanation:
you just divide 245.40 by 30 and is gives 8.18 but you take the decimal away Hope that helps
Find the perimeter of a rectangular garden that has a width of 4x−6 and a length of 2x+4.
Answer:
perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4
Rewrite each explicit formula in the form of a function an = 19 - 7(n - 1)
7. Use this information for the following questions. In 2019, the cost of tuition at a community college was $384per credit hour. The school plans the cost of tuition to rise up to $442 per credit hour in 2022. Round to twodecimal places for all parts of this problem.a. Find the rate of change of the cost of tuition during this time span, write answer as a decimalb. Write a formula for the cost of tuition as a function of the number of years since 2019,c. What will the tuition be in 2025?d. What year will the tuition be $500 per credit hour?
Let:
\(\begin{gathered} (x1,y1)=(2019,384) \\ (x2,y2)=(2022,442) \end{gathered}\)a. The rate of change (the slope) is given by:
\(m=\frac{y2-y1}{x2-x1}=\frac{442-384}{2022-2019}=\frac{58}{3}\approx19.33\)b.
Using the point-slope equation:
\(\begin{gathered} y-y1=m(x-x1) \\ y-384=\frac{58}{3}(x-2019) \\ y-384=\frac{58}{3}x-39034 \\ y(x)=\frac{58}{3}x-38650 \end{gathered}\)c.
\(\begin{gathered} x=2025 \\ y(2025)=\frac{58}{3}(2025)-38650 \\ y(2025)=39150-38650 \\ y(2025)=500 \end{gathered}\)d.
\(\begin{gathered} 500=\frac{58}{3}x-38650 \\ \frac{58}{3}x=500+38650 \\ \frac{58}{3}x=39150 \\ x=2025 \end{gathered}\)In the year 2025
Of the last 20 trains to pull into Lakeside
Station, 14 were full. What is the
experimental probability that the next
train to pull in will be full?
Write your answer as a fraction or whole
number.
P(full) =
The experimental probability that the next train to pull into Lakeside Station will be full is 7/10.
The experimental probability of the next train to pull into Lakeside Station being full can be calculated by dividing the number of times a full train occurred by the total number of trains observed.
Given that out of the last 20 trains, 14 were full, we can express the experimental probability as a fraction:
P(full) = Number of full trains / Total number of trains observed
P(full) = 14 / 20
Simplifying the fraction, we get:
P(full) = 7 / 10
Therefore, the experimental probability that the next train to pull into Lakeside Station will be full is 7/10.
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Find the 22nd term of the sequence described by the
explicit formula:
f(n) = 8 + 3(n - 1)
\(\boxed{\boxed{\pink{\bf \leadsto The \ 22nd \ term \ is \ 71. }}}\)
Step-by-step explanation:Given that the nth term of the Arthemetic Sequence is given by :-
\(\implies f(n) = 8 + 3(n-1) \)
And we need to find the 22nd term .
So in place of n substitute 22 .
\(\bf\implies f(n) = 8 + 3(n-1) \\\\\bf\implies f_{22} = 8 + 3(22-1) \\\\\bf\implies f_{22} = 8 + 3\times 21 \\\\\bf\implies f_{22} = 8 + 63 \\\\\bf\boxed{\bf\implies f_{22} = 71 }\)
Hence the 22nd term is 71 .Evaluate a + 4 when a = 7.
Stuck?
Answer:
11
Step-by-step explanation:
a + 4 when a = 7.
7 + 4 = 11
-TheUnknownScientist
Answer:
11
Step-by-step explanation:
a + 4 = ?
7 + 4 = 11
John spends $2.75 on donuts for his office employees every weekday. On Sunday mornings he takes his wife and kids to the donut shop and spends $12.99. How much money does John spend on donuts throughout the week?
Answer:
26.74
Step-by-step explanation:
add the money John spends on the week days(13.75) to 12.99 and you get your answer
ASAP please!! An American roulette wheel contains 38 slots. Eighteen of the slots are colored red and eighteen
are colored black. The remaining two slots are colored green. A ball is spun on the wheel and comes
to rest in one of the 38 slots. If you bet $1 on the color red and win, the house pays you $1 (even
money).
What is the expected value of betting on red?
Answer:
Step-by-step explanation:
First one 1, can’t bet negative amount of money
A translation maps the point A(-4,7) to the point A'(6,11). Which of the following are the B cordinates of the point B
(4,15) under the same translation
The coordinates of B' are (14, 19) when coordinate of B are (4, 15)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
Translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
Given that after translation the point A(-4,7) to the point A'(6,11)
(x,y)---->(x+10, y+4)
A(-4,7)---->(-4+10, 7+4)=A'(6, 11)
Now we need to find coordinates of B' when B is (4, 15)
(4,15)--->(4+10, 15+4)=(14, 19)
Hence, the coordinates of B' are (14, 19) when coordinate of B are (4, 15)
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A box has 10 red, 5 blue and 5 yellow balls. Draw 6 balls one by one with replacement. Then calculate the probability that
Answer:
I would say its a 16.5 %
Step-by-step explanation:
A game of Blackjack or “21” is played with a regular deck of cards. The aim of the game is to have cards that add up to 21. The cards are not replaced to the deck once they have been drawn. If you draw two cards in a row, what is the probability of getting 21, when first card you get is an ace and the second card is a queen?
The probability of getting 21, when first card is an ace and the second card is a queen = 0.024133.
The term blackjack means that you get a value of 21 with only two cards.
Number of cards in a deck of cards = 52
There are 4 types of cards in a deck of cards - spades, clubs, hearts, and diamonds, out of which spades and clubs are black in colour.
Given that first card is Ace and second one is a Queen.
Odds of getting an Ace are 4/52, odds of the next being Queen is 16/51.
P(blackjack)=4×16/(52/2).
where P is used for probability .
Probability: Probability is simply how likely something is to happen. Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events governed by probability is called statistics.
Probability of getting an ace followed by a queen card: 4/52 * 16/51 = 0.024133.
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Write the number for twenty-one million six hundred thousand
5. What is the area of a rectangle with a length of x-a and a width of x + b? (A) x²-a² (B) x² + b² (C) x² - abx + ab (D) x²-ax-bx - ab (E) x² + bx - ax - ab
'x^2+bx-ax-ab' is the area of a rectangle with a length of x-a and a width of x + b.
What is area of rectangle?
A rectangle basically is a four-sided shape with four right angles. It is one of the most basic shapes in geometry and can be defined by its length and width. The area of a rectangle is the product of its length and width. This measure is typically expressed in square units, such as square feet or square meters. The area of a rectangle can also be found by multiplying the length and width of a given rectangle.
L=x-a
B=x+b
Area of rectangle=?
Area of rectangle=l*b
=(x-a)(x+b)
=x² + bx - ax - ab
Hence, the correct option is Option (E) x² + bx - ax - ab.
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Determine the truth value of each of these statements if the domain for all variables consists of all integers.
a) ∀n∃m(n2 < m)
b) ∃n∀m(n < m2)
c) ∀n∃m(n + m = 0)
d) ∃n∀m(nm = m)
e) ∃n∃m(n2 + m2 = 5)
f ) ∃n∃m(n2 + m2 = 6)
g) ∃n∃m(n + m = 4 ∧ n − m = 1)
h) ∃n∃m(n + m = 4 ∧ n − m = 2)
i) ∀n∀m∃p(p = (m + n)∕2)
For each of the given statements the truth value are as follow:
a. ∀n ∃m (n²< m) is False.
b. ∃n ∀m (n < m²) is true.
As given in the question,
Domain of all the presents variables consists of integers.
Truth value for the given statements are as follow:
a. ∀n ∃m (n²< m)
For integers -2
(-2)² = 4
There is no such integer present whose square is less than the integer.
Truth value of above statement is false.
b. ∃n ∀m (n < m²)
For integers -3
(-3)² = 9
-3 < 9 is the true for all positive and negative integers.
Therefore, the truth value of the given statements are as follow:
a. ∀n ∃m (n²< m) is False.
b. ∃n ∀m (n < m²) is true.
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Could you solve for `x` using any tools we have so far? Why or why not?
the value of x can be calculated using the given data.
What are the properties of a Triangle?The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.
Given a triangle, with two known angles of 42-degree and 26-degree
Let the triangle be ABC
This is, in fact, exactly what the Law of Sines tells you:
a/sinA = b/sinB = c/sinC = m
where m is that scale factor and also the diameter of the triangle's circumcircle.
in our case,
∠A = 26°
∠B = 42°
thus,
a/sinA = b/sinB
4/sin26 = b/sin42
b = 4* (sin 42 /sin26)
b =6.12
or x = 6.1 cm
therefore, the value of x can be calculated using the given data.
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10 - 5 2/3 = ? i need this for math
\(\huge\color{purple}\boxed{\colorbox{black}{♡Solution♡}}\)
\(4 \frac{1}{3} \) ✅Step-by-step explanation:
\(10 - 5 \frac{2}{3} \\ = 10 - \frac{17}{3} \\ = \frac{10 \times 3}{1 \times 3} - \frac{17}{3} \\ = \frac{30 - 17}{3} \\ = \frac{13}{3} \\ = 4 \frac{1}{3} \)
\(\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}\)
Graph the line that passes through the points (0, -5) and (5, 1) and
determine the equation of the line.
y
10
9
00
7
6
5
4
Answer:
y = 10/1x - 5
Step-by-step explanation:
y=mx+b
m=slope b=y-intercept
therefore
y=10/1x -5
(10/1 is a fractions just too lazy to make it a fraction on here)
Evaluate the expression: −(8 − 12) + 60 + (−4)2.
Answer: 80
Step-by-step explanation:
⇒ −(8 − 12) + 60 + (−4)²
⇒ -(-4) + 60 + 16
⇒ 4 + 60 + 16
⇒ 80
A health club charges a one-time sign-up fee and a monthly membership fee. The
equation y = 28x + 50 represents what the health club charges. Find the rate of
change.
Answer:
The rate of change is 28.
Step-by-step explanation:
The equation is in slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept.
a student spends 18 out of 35 of his pocket money on transport and fruit what is the fraction left?
To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.
The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.
Therefore, the fraction of pocket money left can be written as 17/35.
2/3x-5=-13 please help solve
Answer: -12
Step-by-step explanation:
Equation:
2/3x-5=-13
1.
Move -5 to the other so it becomes positive
2/3x=-13+5
-13+5=-8, Therefore
2/3x=-8
2.
x=-8 divided by 2/3 (can’t type the division sign)
(optional, you can convert -8 into -8/1 because 2/3 is a fraction, I will be doing this to make it easier **just a tip :)**)
3.
Find the reciprocal of 2/3 and multiply -8/1 by 3/2
4.
-8/1*3/2=-24/2=-12
Hoped this helped!!
I operate a small convenience store. Typically, from 10 am to 11 am, I get 23 customers. What is the standard deviation of the number of customers that might check out between 10.15 am and 10.30 am
Answer:
The standard deviation of the number of customers that might check out between 10.15 am and 10.30 am is 2.4.
Step-by-step explanation:
We have the mean during a time interval, so the Poisson distribution is used.
Poisson distribution:
In the Poisson distribution, the standard deviation is the square root of the mean.
Typically, from 10 am to 11 am, I get 23 customers.
In an hour, you get 23 customers.
What is the standard deviation of the number of customers that might check out between 10.15 am and 10.30 am?
In this period, there are 15 minutes, that is, one fourth of an hour, so:
\(\mu = \frac{23}{4} = 5.75\)
And the standard deviation will be the square root of the mean, so:
\(\sigma = \sqrt{5.75} = 2.4\)
The standard deviation of the number of customers that might check out between 10.15 am and 10.30 am is 2.4.