Find factors of x^2 and 72, that, when combined, will give you 17x
x ^2 + 17x + 72
x 9
x 8
(x + 9)(x + 8) is your factor.
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Let u = <6, -9>, v = <1, -4>. Find u - v.
A) <5, -5>
B) <10, -10>
C) <15, 5>
D) <7, -13>
u - v = <6 - 1, -9 - (-4)> = <5, -5> . . . . . . . matches selection A)
_____
The sum or difference of vectors is simply the sum or difference of corresponding coordinates.
Determine if the columns of the matrix form a linearly independent set. justify your answer. left bracket start 4 by 3 matrix 1st row 1st column negative 2 2nd column negative 1 3rd column 0 2nd row 1st column 0 2nd column negative 1 3rd column 3 3rd row 1st column 1 2nd column 1 3rd column negative 6 4st row 1st column 2 2nd column 1 3rd column negative 12 endmatrix right bracket −2 −1 0 0 −1 3 1 1 −6 2 1 −12
Convert 64°F to °C (to the nearest tenth) using one of the following formulas: Fahrenheit to Celsius Celsius to Fahrenheit °C = (°F - 32) × °F = × °C + 32.
HELP!
a. 17.8°
b. 54.2°
c. 72.0°
d. 161.6°
The answer is 17.8° C
Step-by-step explanation:In order to Convert Fahrenheit to centigrade scale we use the formula
°C = (°F - 32) × 5/9
So putting the values in the equation we get
(64°F − 32) × 5/9 = 17.778°C
A young company expects to double their profits every year for the next ten years. If their profits were $5,000 this year, which expression represents their profits after ten years?
a) 5,000 × 2 × 10
b) 5,000 × 210
c) 5,0002 × 10
d) 5,00010
An asteroid has hit the Earth and created a huge crater. Engineers and scientists hove measured around the crater to be 79.5 miles. How much of the surfoce of the Earth hos been effected by the crater impact?
To determine the affected area by an asteroid impact, calculate the radius from the circumference of the crater and then the area of the circle. The estimated crater area from a 79.5-mile circumference is approximately 506.7 square miles, indicating the surface area affected.
Explanation:To estimate how much of the Earth's surface has been affected by the asteroid impact that resulted in a crater with a measured circumference of 79.5 miles, we need to recognize that this measurement refers to the circumference of a circle (the crater). We use the circumference to find the radius of that circle, and then calculate the area of the circle to understand the extent of the impact.
First, we calculate the radius (r) of the crater using the circumference (C): C = 2πr. Plugging in the known circumference, r = C / (2π), so r = 79.5 miles / (2 × 3.14), which approximates to 12.7 miles. Moving forward, we can now find the area (A) of the crater using A = πr². Squaring the radius gives us [tex](12.7)^2[/tex] and then multiplying by π gives us approximately 506.7 square miles.
The actual crater area accounting for the circular shape is approximately 506.7 square miles, which roughly indicates the immediate surface area affected by the impact. It's noteworthy that the surrounding ecosystem and earth's surface may also experience indirect effects extending beyond this area.
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its cost $75.00 dollars to rent the laser tag center ,plus 11.50 per person what will be the total cost to rent the laser tag center for 15 people
Answer:
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Step-by-step explanation:
Pierre's parents ordered some pizzas for a party. 4.5 pizzas were eaten at the party. There were at least 5 1/2 whole pizzas left over. How many pizzas did pierre's parents order?
A rectangle prism has length of 20 inches, a width of 2 inches and height of 3 1/4 inches. The prism is filled with cubes that have edge lengths of 1/4 inches. How many cubes are needed to fill the rectangle?
Winners of the georgia lotto drawing are given the choice of receiving the winning amount divided equally over 2222 years or as a lump-sum cash option amount. the cash option amount is determined by discounting the annual winning payment at 44% over 2222 years. this week the lottery is worth $33 million to a single winner. what would the cash option payout be?
To calculate the cash option payout, we need to discount the annual payment at a rate of 44% over 2222 years using the present value formula. The cash option payout would be approximately $2,938,624.13.
Explanation:To determine the cash option payout, we need to calculate the present value of the annuity. The annual payment is the total amount of the lottery prize divided by the number of years, which is $33 million / 2222 = $14,808.81. To discount this amount at a rate of 44% over 2222 years, we can use the formula:
PV = Payment / ((1 + r)^n - 1) * (1 - (1 / (1 + r))^n)
where PV is the present value, Payment is the annual payment, r is the discount rate (0.44), and n is the number of years (2222). Plugging in the values, we get:
PV = $14,808.81 / ((1 + 0.44)^2222 - 1) * (1 - (1 / (1 + 0.44))^2222)
Solving this equation gives us the cash option payout, which is approximately $2,938,624.13.
if 5ml=1 tsp, how many teaspoons are in 85ml
G find z such that 9.0% of the standard normal curve lies to the right of z. (round your answer to two decimal places.)
The common stock of the downtowne should return 23 percent in a boom, 16 percent in a normal economy, and lose 32 percent in a recession. the probabilities of a boom, normal economy, and recession are 5 percent, 90 percent, and 5 percent, respectively. what is the variance of the returns on this stock?
a..012453
b..012914
c..011345
d..011663
e..012691
Which is the measure of AB? 10 feet 15 feet 20 feet 100 feet
12. Which one of the following is a geometric sequence?
A. −7, 10, 23, 36, . . .
B. 8, 4, 2, 1, 1/2, 1/4, . . .
C. 2, −3, 9/2, −18/4
D. 0, 1, 2, 3, . . .
Answer:
B. 8, 4, 2, 1, 1/2, 1/4, . . .Step-by-step explanation:
A geometric sequence or geometric progression is a sequence where each term after the first one can be found by multiplying a certain factor.
So, basically, to find the geometric sequence, we just need to divide the second term by the first term and observe if it results a constant factor.
By doing that, we observe that the second equence is a geometric sequence with a reasonf of 1/2, let's demonstrate it
[tex]8\times \frac{1}{2}= 4 (second \ term)\\4 \times \frac{1}{2}=2 (third \ term)\\ 2 \times \frac{1}{2}= 1 (fourth \ term)\\ 1 \times \frac{1}{2}= \frac{1}{2} (fiftg \ term)\\ \frac{1}{2} \times \frac{1}{2}= \frac{1}{4} (sixth \ term)[/tex]
As you can observe, we perfectly built the sequence is its ratio or factor.
Therefore, choice B is a geometric sequence.
In August cory begins school shopping for his triplet daughters. one day he bought 10 pairs of socks for $2.50 each and 3 pairs of socks for d dollars each. He spent a total of 135.97 write and solve an equation to find the cost of one pair of shoes
According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica’s z-score? (Round your answer to TWO decimal places.)
A radar gun used to determine the speed of passing cars must be within 7 mph of the actual speed of a selected car. If a highway patrol officer reads a speed of 59 mph for a car, does he have irrefutable evidence that the car was speeding in a 55 mph zone?
Fran made 8 cups of potato soup in a big pot, then served 4 bowls of soup to her family. each bowl holds 6 fluid ounces. how much soup was left in the pot
Eight soccer players share 7 oranges. How would this be as a fraction?
passes thru ( 7, -5) and has m=0
x^2+1/2x+1/16=4/9 Factor the perfect-square trinomial on the left side of the equation. (x + )² = 4/9
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we have
[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}[/tex]
we know that
[tex](x+a)^{2}=x^{2}+2ax+a^{2}[/tex]
in this problem
[tex]2ax=\frac{1}{2}x[/tex] ------> [tex]a=\frac{1}{4}[/tex]
[tex]a^{2}=\frac{1}{16}[/tex] -----> [tex]a=\frac{1}{4}[/tex]
so
[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=(x+\frac{1}{4})^{2}[/tex]
the missing number in the left side is [tex]\frac{1}{4}[/tex]
At a florist's shop two assistants made 13 flower arrangements in a certain amount of time. Assuming all assistants will work for the same amount of time and each assistant is trained to work at the same rate, how many assistants are needed to make: 195 arrangements
Number of assistants required to make 13 flower arrangements = 2
Let us use unitary method here.
Number of assistants required to make 1 flower arrangements = 2/13
Number of assistants required to make 195 flower arrangements = 2/13 *195 =30
Answer : So 30 assistants are required to make 195 flower arrangements.
A paperweight in the shape of a rectangular pyramid is shown:If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex,which shape describes the cross section
Answer:
The correct answer is a triangle will be formed.
Step-by-step explanation:
If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex, the resulting figure will have 3 sides or vertices. Hence, this shape will be a triangle. The triangle only forms if it does pass through the top vertex.
So, triangle is the answer.
If n = 10 and p = 0.70, then the standard deviation of the binomial distribution is
The standard deviation for the given binomial distribution is 1.449.
What is binomial distribution?A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution.
Formula for the calculation of standard deviationσ = [tex]\sqrt{nP(1 -P)}[/tex]
where,
σ is the standard deviation
n is the number of trials in the binomial experiment.
P is the probability of success on an individual.
According to the given question we have,
The number of trials in the binomial experiment, n = 10
The probability of success on an individual, p = 0.70
Therefore, the standard deviation is given by
σ = [tex]\sqrt{10(0.70)(1 -0.70)} = \sqrt{7(0.3)}=\sqrt{2.1} =1.449[/tex]
Hence, the standard deviation for the given binomial distribution is 1.449.
Learn more about the binomial distribution here:
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On a standardized exam for high school seniors in 2013, the mean scale for the mathematics portion of the exam was 514 and the standard deviation was 118. If the scores for this exam are approximately normally distributed, what percent of students taking the exam received a scale score between 396 and 632? Express your answer as a whole percent.
Use the alternating series estimation theorem to estimate the range of values of x for which the given approximation is accurate to within the stated error. check your answer graphically. (round your answers to three decimal places.) sin(x) ≈ x − x3 6 |error| < 0.000001
The approximation sin (x) = x - x^3/6 has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].
What is alternating series?In mathematics, the alternating series is an infinite series of a term in the form of
[tex]{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n}a_{n}} \\{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}{\displaystyle \sum _{n=0}^{\infty }(-1)^{n+1}a_{n}}[/tex]
The expansion series of sin(x)
[tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!} +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +..[/tex] (a)
the given approximation [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex] (b)
So, the approximation error term =(b)-(a)
[tex]\rm = -[ +\frac{x^{5} }{5!} -\frac{x^{7} }{7!} +\frac{x^{9} }{9!}-....]\\\rm = -\frac{x^{5} }{5!} +\frac{x^{7} }{7!} -\frac{x^{9} }{9!}+....[/tex]
The alternative series theorem states that we need to ensure that the absolute value of the first term [tex]\rm \frac{x^{5} }{5!}[/tex]less than the error limit, For that the sum will be below the error limit, which means
[tex]\rm \frac{x^{5} }{5!}[/tex] < 0.000001
Solving for x, we get
x [tex]\rm x^{5} = 5! \times 0.000001\\ = 0.000120\\\rm = 0.000120^{1/5} \\ = 0.164375[/tex]
Therefore, the approximation [tex]\rm sin (x) = \frac{x}{1!} -\frac{x^{3} }{3!}[/tex] has an absolute error below 0.000001 for the interval [-0.164375,+0.164375].
by checking
[tex]\rm sin(0.164375)-(0.164375)^{3/3!} \\= 9.993513\times10^{-7} < 0.000001[/tex]
Learn more about alternating series;
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A patio has the shape of the quadrilateral drawn in the picture below.
1) Find the area of the patio.
2) What is the minimum number of square-tiles with sides of 30 cm that are needed to cover the patio if 10% more tiles will be needed to cover the non-rectangular shape of the patio?
The line segments AC and CE break this quadrilateral into three triangles. The area of a triangle is given by A=1/2bh. The base of ΔADC is 6 and the height is 4.5; A=1/2(6)(4.5)=13.5m².
To find the area of ΔACE, we must first find the length of segment AE. To do this, we will need to know both EC, which we are given, and AC, which we are not. We will use the Pythagorean theorem for ΔADC to find the length of AC.
6²+(4.5)²=(AC)²
36+20.25=(AC)²
56.25=(AC)²
√56.25=√(AC)²
7.5=AC
Now that we know the length of AC, we will use the Pythagorean theorem on ΔACE to find the length of AE:
7²+(AE)²=(7.5)²
49+(AE)²=56.25
49+(AE)²-49=56.25-49
(AE)²=7.25
√(AE)²=√7.25
AE≈2.69
Now we can find the area of ΔACE: A=1/2(7)(2.69)=9.415m²
To find the area of ΔBCE, we need to find the length of EB. We know that AB=9 and AE=2.69. Subtracting those two, we find the length of EB to be 6.31m. Therefore the area of ΔBCE=1/2(6.31)(7)=22.085m²
The total area is given by adding these three together:
13.5+9.415+22.985=45m².
It would take 15 rows of 20 tiles each to cover the rectangular portion of this patio (4.5m*100 =450cm; 450cm/30-cm tiles = 15 rows of tiles; 6m*100=600cm; 600cm/30-cm tiles = 20 tiles per row) which comes out to 300 tiles. However, adding an extra 10% to that:
300*0.1+300=30+300=330 tiles.
There is only one granola bar left out of a pan of 10 bars. if Will and Rachel decide to split the last granola bar what fraction of the entire pan of granola bars will each friend receive?