Answers
Selection A is appropriate.
Related Questions
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1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?
A. 5.88 x 10^13 miles
B. 5.76 x 10^14 miles
C. 5.88 x 10^12 miles
D. 9.8 x 10^12 miles
2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?
A. $4,979.11
B. $14,920.54
C. $112,992.00
D. $15,494.70
Answers
Answer:
1. B. 5.76 × 10¹⁴ miles.
2. D. $15,494.70
Step-by-step explanation:
Question 1: We have,
Distance light traveled in one year = 5.88 × 10¹² miles.
Since, the star is 9.8 × 10¹ light years away.
So, we get,
Total number of miles the star is away = 5.88 × 10¹² × 9.8 × 10¹ = 57.62 × 10¹³ miles.
Hence, the total number of miles are 5.76 × 10¹⁴ miles.
Question 2: We have,
Principle amount, P= $1,600
Rate of interest, r = 7% = 0.07
Time period, t = 33 years
Moreover, the interest is compounded twice per year i.e. n=2.
Since, Amount = [tex]P(1+\frac{r}{n})^{nt}[/tex]
i.e. Amount = [tex]1600(1+\frac{0.07}{2})^{2\times 33}[/tex]
i.e. Amount = [tex]1600(1+\frac{0.035)^{66}[/tex]
i.e. Amount = [tex]1600(1.035)^{66}[/tex]
i.e. Amount = [tex]1600\times 9.68418}[/tex]
i.e. Amount = $15,494.70
Hence, the balance in the account is $15,494.70.
When dividing which number goes first in the calculator?
Answers
so the number of chocolate pieces ÷ by number of people
e.g: 6 pieces of chocolate ÷ 3 people
6÷2 = 3
however you can also divide the other way round. by dividing the smaller number first. this means u are diving a small amount to even smaller amounts.
2÷4 = 1/2
On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis. What are the coordinates of Q and S?
Answers
Answer:
Q(2, −1), S(−6, 5)
Step-by-step explanation:
The original ordered pairs were (2, 1) and (−6, −5). When you reflect across the x-axis the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
so since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hope this helped fellow FLVS student!!
The coordinates are Q(2, −1) and S(−6, 5)
What is reflection of points?A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.
Given that, On a coordinate grid, point P is at (2, 1) and point R is at (−6, −5). Points Q and S are a reflection of both points across the x-axis.
We know that, when you reflect across the x-axis, the x-coordinates of the two ordered pairs are the same, and the y coordinate is the opposite in sign (positive and negative).
So, since the original ordered pairs were (2, 1) and (−6, −5), the reflected ordered pairs would be Q(2, −1), S(−6, 5) because the y-coordinates are different and the x-coordinates are the same.
Hence, The coordinates are Q(2, −1) and S(−6, 5)
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The base of a parallelogram is 24 inches longer than three times the height. The area of the parallelogram is 384 square inches. What is the height?
The height is x = ________ inches.
Answers
To find the height of the parallelogram, set up the equation (3x + 24) x = 384 using the formula for the area of a parallelogram. Solve the resulting quadratic equation to find that x, representing the height, is 8 inche
The student is trying to find the height of a parallelogram when the base is 24 inches longer than three times the height and the area is 384 square inches. Let the height of the parallelogram be represented by x inches. According to the problem, the base (b) is 3x + 24 inches. Using the formula Base x Height = Area of parallelogram, we can set up the equation:
(3x + 24) x= 384
Now solve for x using the distributive property:
3x^2 + 24x = 384
Next, set the equation to zero:
3x^2 + 24x - 384 = 0
Divide the entire equation by 3 to simplify:
x^2 + 8x - 128 = 0
Factor the quadratic equation:
(x + 16)(x - 8) = 0
Set each factor equal to zero:
x + 16 = 0 or x - 8 = 0
Since the height cannot be negative, x = 8 is the solution. Therefore, the height of the parallelogram is 8 inches.
The vertical height of a right circular conical tent is 4m and the volume of space inside it is 968/7 cubic metre. Find the canvas required to make the tent.
Answers
v = 1/3 * height * area of the base
= 1/3 ×hπr²
where v - volume
h - height of the conical tent
r - radius of base circle
area of the base = 3v/h
πr² = 3 *968/7 m³ /4 m
r² = 3 * 968 * 7 / (7 * 22* 4 )
= 33
r = 5.74 m
area of the curved surface = πrl
where l is the slant height
l² = r² + h²
= 5.74² + 4²
= 33 + 16
= 49 m
l = 7 m
then the area of the curved surface is ;
area = πrl
= (22/7) * 5.74 * 7
= 126.28 m²
the canvas should have area 126.28 m² to cover the tent
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?
The graph of f(x) = x2 is widened.
The graph of f(x) = x2 is shifted left 3 units.
The graph of f(x) = x2 is shifted up 30 units.
The graph of f(x) = x2 is reflected over the x-axis.
Answers
We know that the graph of f(x) is NOT widened, because for a number c greater than 1, cf(x) stretches the graph vertically, not horizontally.
We know that the graph of f(x) is NOT shifted up 30 units. It is tempting to say this because we do see +30 as the last term. But, we have to calculate the vertex of g(x). If we find the point [tex]P( \frac{-b}{2a}, g(\frac{-b}{2a}))[/tex], that is, by taking doing [tex] \frac{-24}{2*4} = -3[/tex], [tex]g(-3)=-6[/tex], we see that the vertex is six units down from f(x), not 30 units up!
We know that the graph of f(x) is NOT reflected over the x-axis, because there would need to a negative coefficient on the [tex]x^2[/tex]-term, and there isn't.
We know that the graph of f(x) IS shifted 3 units to the left. When we calculated the vertex earlier, we saw that it is [tex](-3,6)[/tex], which indeed corresponds to a shift 3 units to the left from the origin.
The graph of f(x) = x2 is shifted left 3 units.
find the measure of side c.
Answers
The length of side AB (c) in triangle ABC is 31.38 m.
In triangle ABC, angle BCA is a right angle with a measure of 90 degrees, and angle CAB has a measure of 42 degrees.
The side BC has a length of 21 m and the side AB has a length of c.
To find the length of side c, we can use the trigonometric function sine.
By using the sine function and the given angle CAB, we can calculate the length of side c as follows:
c = AB = BC * sin(CAB) = 21 * sin(42) = 31.38 m
Therefore, The length of side AB (c) in triangle ABC is 31.38 m.
The probable question may be:
In triangle ABC, Angle BCA= 90 degree, angle CAB=42 degree, Side BC (a)=21 m, Side AB=c, find the measure of side c.
The solution set for 7q2 − 28 = 0 is { }. (Separate the solutions with a comma) NextReset
Answers
7q^2 = 28
q^2 = 4
q = +/-2
solution set is {-2,2}
Answer:
{ 2,-2}
Step-by-step explanation:
In order to solve this set we just have to first clear the "q":
[tex]7q^{2} -28=0\\7q^{2} -28+28=+28\\7q^{2} =28\\\frac{7q^{2}}{7} =\frac{28}{7} \\q^{2}=4\\\sqrt{q^{2}} =\sqrt{4} \\q= 2, -2[/tex]
So as we know the solution for a square root is always a negative and positive number, so the solutions ser for 7q2-28=0 is 2 and -2
BC is tangent to circle A at B and to circle D at C. AB= 10 BC= 21 DC= 8 find AD to the nearest tenth
Answers
If there are other details, please post.
The distance AD is found by Pythagoras theorem, with
AD=sqrt(BC^2+(AB-DC)^2)=sqrt(21^2+2^2)=sqrt(441+4)=sqrt(445)
=21.095 (to the third decimal place)
What are the roots of the polynomial equation?
–12, 12
–4, 3
–3, 4
–1, 1
Answers
We have that in this case, the functions intersect in:
x = -3
x = 4
Therefore the roots of the polynomial are:
x = -3
x = 4
Answer:
-3, 4 (option 3)
police can estimate the speed of a vehicle before the brakes are applied using the formula 0.75d = s^2 / 30.25 where is the speed in miles per hour d is the length of the vehicle's skid marks. What was the approximate speed of a vehicle that left a skid mark measuring 160 feet?
1.about 36 miles per hour
2."" 60 ""
3."" 13 ""
4"" 54 ""
Answers
We also know from our problem that the vehicle left a skid mark measuring 160 feet, so [tex]d=160[/tex]. Lets replace that value in our formula to find the speed [tex]s[/tex]:
[tex](0.75)(160)= \frac{s^{2} }{30.25} [/tex]
[tex]120= \frac{s^{2} }{30.25} [/tex]
[tex](120)(30.25)=s ^{2} [/tex]
[tex]s ^{2} =3630[/tex]
[tex]s= \sqrt{3630} [/tex]
[tex]s=60.25[/tex]
We can conclude that the speed of the car before the brakes were applied was about 60 miles per hour.
The answer would be ≈60mph, hence the answer is B.
suppose you invest $500 in a savings account that pays 3.5% annual interest. when will the account contain $650
Answers
Each trapezoid in the figure below is congruent to trapezoid ABDC.
What is the perimeter of hexagon ACEFGH?
1)28 cm
2)32 cm
3)36 cm
4)64 cm
Answers
Answer:
The answer is the second option
[tex]32\ cm[/tex]
Step-by-step explanation:
we Know that
Each trapezoid in the figure below is congruent to trapezoid ABDC
so
[tex]CE=AC=3\ cm[/tex]
[tex]EF=AB+CD=4+6=10\ cm[/tex]
[tex]FG=AC=3\ cm[/tex]
[tex]GH=AC=3\ cm[/tex]
[tex]AH=AB+BH=AB+CD=4+6=10\ cm[/tex]
the perimeter is equal to
[tex]P=AC+CE+EF+FG+GH+AH[/tex]
substitute the values
[tex]P=3+3+10+3+3+10=32\ cm[/tex]
Which ordered pair will be the solution for the function y = 12 - x?
(7, 4)
(6, 6)
(4, 9)
(2, 14)
Answers
The solution to the function y = 12 - x is the ordered pair (6, 6) because when we substitute x = 6 into the function, the result, y, is also 6, which matches the given y-value in the pair.
Explanation:To find the ordered pair that is a solution for the function y = 12 - x, we need to substitute the x-values of each given ordered pair into the equation and see which one gives a resulting y-value that matches the one in the pair.
(7, 4): y = 12 - 7 = 5 – This does not match the y-value of 4.(6, 6): y = 12 - 6 = 6 – This is correct, as it matches the y-value of 6.(4, 9): y = 12 - 4 = 8 – This does not match the y-value of 9.(2, 14): y = 12 - 2 = 10 – This does not match the y-value of 14.Therefore, the solution to the function is the ordered pair (6, 6).
What is the value of n?
Enter your answer in the box.
n =____m
Answers
Function f, shown below, is translated down 3 units and left 4 units to create function g. f(x)=3|x-2|-5. Fill in the values of a, h, and k to write function g.
Answers
We consider two kinds of transformations.
Vertical and horizontal displacements: It is assumed that c is a positive constant, ie c> 0 and y = f (x) then
y = f (x) + c moves the graph c units up.
y = f (x) - c moves the graph c units down.
y = f (x + c) shifts the graph c units to the right.
y = f (x - c) shifts the graph c units to the left.
We have then:
f (x) = 3 | x-2 | -5
Is down 3 units
f (x) = 3 | x-2 | -5 -3
and left 4 units
f (x) = 3 | (x-4) -2 | -5 -3
Rewriting
g (x) = 3lx-6l-8
Answer:
g (x) = 3lx-6l-8
Answer:
g (x) = 3lx+2l-8
Step-by-step explanation:
Carlosego made a mistake on the horizontal shift.
y = f (x + c) shifts the graph c units to the left.
Therefore, g (x) = 3lx - 2 + 4l - 8 is
g (x) = 3lx+2l-8
The least common denominator of two fractions is 30. If you add the two denominators, their sum is 17. What are the denominators?
Answers
x*y=30
It should be 15 and 2
A company has found that the demand for its product varies inversely as the price of the product. when the price x is 3.5 dollars, the demand yy is 450 units. find a mathematical model that gives the demand y in terms of the price x in dollars.
Answers
y = k/x ; where k is constant.
inverse relationship means when one variable increases, the other decreases.
y represents the demand
x represents the price
450 = k/3.5
k = 450 * 3.5
k = 1,575
The mathematical model that gives the demand y in terms of the price x in dollars is:
y = 1575 / x
The mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.
Explanation:To find a mathematical model that gives the demand, y, in terms of the price, x, we can use the formula for inverse variation. Inverse variation is described by the equation y = k/x, where k is a constant. To find the value of k, we can use the given information: when x = 3.5, y = 450. Substituting these values into the equation, we get 450 = k/3.5. Solving for k, we find that k = 1575. Therefore, the mathematical model that gives the demand, y, in terms of the price, x, is y = 1575/x.
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50 POINTS!!!! NEED HELP!!! 2 QUESTIONS!!!! please answer correctly. i begging u
♦Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawson's annual premium? Use the table.
♦Rachel, a 45-year-old female, bought a $120,000, a 20-year life insurance policy through her employer. Rachel is paid biweekly. How much is deducted from each of her paychecks for life insurance? Use the Table.
Answers
Rachel's checks I believe would have a deduction of $63.14.
♦Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawson's annual premium? Use the table.
Dawson is 42, with a 20 year premium coverage, which will amount to $13.68 per $1000. Multiply $13.68 with 180 (because there are 180 $10,000)
13.68 x 180 = $2462.40
annual premium = $2462.40
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To solve the next one, Rachel bought a 20 year life insurance, which amounts to $17.56 per $1000
$63.14 is your answer
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hope this helps
Ava rounded 19,350 to the nearest thousand and got 20,000. Which of the following statements is true? Ava rounded correctly. Ava rounded incorrectly; the answer should be 19,400. Ava rounded incorrectly; the answer should be 19,000. Ava rounded incorrectly; the answer should be 19,300.
Answers
Since we are rounding to the nearest thousand and 350 < 500, we round down to 19000.
Hope this helped!
How many real number solutions exist for 2x2 + 8x + 8 = 0?
Answers
There is one solution with multiplicity 2.
[tex]2x^2+8x+8=0\\ 2(x^2+4x+4)=0\\ 2(x+2)^2=0\\ Sol=\{ {-2}\} [/tex]
Final answer:
There are no real number solutions for the given equation.
Explanation:
The given equation is 2x² + 8x + 8 = 0. To find the number of real number solutions for this equation, we can use the discriminant of the quadratic equation. The discriminant is given by the formula D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 2, b = 8, and c = 8. Substituting these values into the formula, we get D = 8² - 4(2)(8) = 16 - 64 = -48.
Since the discriminant is negative (-48), there are no real number solutions for the equation. Therefore, the answer is 0.
A small tree was planted at a height of 10 feet. The tree has been planted for 14 months, and is now 49.2 feet tall. Which equation could be used to find x, the average number of feet the tree grew each month?
Answers
A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
A)53.53 feetB)74.62 feetC)126.11 feetD)322.75 feet
Answers
Tan(α)=Opposite leg/Adjacent leg
α is the angle of elevation (α=67°).
The opposite leg is the height of the pole. Let's call it "x".
Adjacent leg=137 feet
When you substitute these values into the formula Tan(α)=Opposite leg/Adjacent leg, you have:
Tan(α)=Opposite leg/Adjacent leg
Tan(67°)=x/137
You must clear the "x"
x=137xTan(67°)
x=322.75
What is the height of the pole?
The answer is: The height of the pole is 322.75 feet.
Make this equation true by rearranging the numbers.... 26=74
Answers
FALSE
Jerry goes to the bank and borrows $9,000 for farm equipment. The simple yearly interest is 9.5% and he pays off the loan over a period of 2 years with 24 equal monthly payments. What’s Jerry’s monthly payment
Answers
Jerry's monthly payment can be calculated using the formula for the monthly payment on a loan. Plugging in the given values will give the exact monthly payment amount.
Explanation:To calculate Jerry's monthly payment, we can use the formula for the monthly payment on a loan:
Monthly Payment = P × r × (1 + r)^(n) / ((1 + r)^(n) - 1)
Where:
P is the principal amount borrowed, which is $9,000r is the monthly interest rate, which is calculated by dividing the annual interest rate by 12 and converting it to a decimal. In this case, it would be 9.5% / 12 = 0.0079 (rounded to four decimal places)n is the total number of payments, which is 2 years × 12 months = 24 monthsPlugging in the values:
Monthly Payment = $9,000 × 0.0079 × (1 + 0.0079)^(24) / ((1 + 0.0079)^(24) - 1)
Simplifying this equation will give us the monthly payment amount.
A rectangle is 1/3 yards long and 2/3 yards wide. What is the area of the rectangle? Enter your answer in the box as a fraction in simplest form.
Answers
To find the area of a rectangle, multiply the length by the width. For a rectangle that is 1/3 yards long and 2/3 yards wide, the area is 2/9 square yards, which is the answer in simplest form.
The question asks us to calculate the area of a rectangle that is 1/3 yards long and 2/3 yards wide. The formula to compute the area of a rectangle is length imes width.
First, multiply the length and the width:
Length: 1/3 yards
Width: 2/3 yards
Area = (1/3) times (2/3) yards sq
Area = 2/9 square yards
This is the simplest form of the fraction, so this is the final answer: The area of the rectangle is 2/9 square yards.
helpppppppppppppppppppppppp
Answers
We can write it as:
[tex] \sqrt{-1} \times \sqrt{80} [/tex]
Apply imaginary number rule:
[tex] \sqrt{-1} =i[/tex]
We get
[tex] =\sqrt{80} i[/tex]
Now factorise 80.
80=4 x 4 x 5 = 4² x 5
[tex] \sqrt{80}i = \sqrt{4^2 \times 5} i [/tex]
[tex] =\sqrt{4^2} \times \sqrt{5} i \\ =4 \sqrt{5} i[/tex]
[tex]Answer: \ 4 \sqrt{5} i[/tex]
We then have to rewrite:
root (-80)
root (- (16 * 5))
4raiz (-5)
Then remember that:
Root (-1) = i
We have then:
4raiz (5) i
Answer:
The equivalent expression is:
4raiz (5) i
(option 3)
The sum of the first 30 terms of the sequence an=6n+5 is
Answers
second term = 12+5 = 17
common difference = 6
Sum of n terms:-
Sn = (n/2) [ 2a1 + d(n - 1)]
Sum of 30 terms:-
S30 = (30/2)[ 2*11 + 6(30-1)]
= 15 * ( 22 + 174)
= 15 * 196
= 2940 Answer
Answer:
[tex]S_{30}=2940[/tex].
Step-by-step explanation:
Given : [tex]a_{n} =6n+5[/tex].
To find : The sum of the first 30 terms .
Solution: We have given [tex]a_{n} =6n+5[/tex].
For n = 1
[tex]a_{1} =6(1)+5[/tex].
[tex]a_{1} =6+5[/tex].
[tex]a_{1} =11[/tex].
For n =2
[tex]a_{2} =6(2)+5[/tex].
[tex]a_{2} =17[/tex].
Common difference = 17 - 11 = 6.
Sum of nth term : [tex]S_{n} =\frac{n}{2}[2a+(n-1)d][/tex].
d = common difference = 6.
For n = 30 .
[tex]S_{30} =\frac{30}{2}[2(11+(30-1)6][/tex].
[tex]S_{30} =15[22+29 *6][/tex].
[tex]S_{30} =15[22+29 *6][/tex].
[tex]S_{30} =15[22+174][/tex].
[tex]S_{30} =15[196][/tex].
[tex]S_{30}=2940[/tex].
Therefore, [tex]S_{30}=2940[/tex].
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Answers
The math test scores of Mrs. Hunter's class are shown below. 48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100 What is the range of the scores? A) 44 B) 52 C) 54 D) 62
Answers
The range of the scores is B) 52.
What is the range of the function?The range of a function is defined as the set of all the possible output values that are valid for the given function.
Since the range would be the difference between the highest and the lowest score
WE are given that the math test scores of Mrs. Hunter's class are shown below.
48, 56, 68, 72, 72, 78, 78, 80, 82, 84, 88, 88, 88, 90, 94, 98, 100
Highest = 100
lowest = 48
here, we have,
range = 100 - 48 = 52
Hence, The solution is, range = 52.
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