Answer:
y = - [tex]\frac{1}{3}[/tex] x + 8
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 )
Rearrange 3x - y = 9 into this form by subtracting 3x from both sides
- y = - 3x + 9 ( divide all terms by - 1 )
y = 3x - 9 ← in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{3}[/tex], thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (6, 6) into the partial equation
6 = - 2 + c ⇒ c = 6 + 2 = 8
y = - [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line
Which of the following is a complex number?
Answer:
The correct answer is B.
The triangular pyramid has identical equilateral triangles as its faces. Find the surface area of the pyramid.
Alternative Text
A. 113.4 ft2
B. 140.4 ft2
C. 226.8 ft2
D. 631.8 ft2
Answer:
B. 140.4 square feet.Step-by-step explanation:
If all faces are equilateral, and they are all congruent, that means the surface area of the pyramid is formed by 4 equal triangles, including the base.
We just need to find the area of one triangle and then multiply it by 4.
According to the image, the height of a triangle face is [tex]h=7.8 \ ft[/tex], and its base is [tex]b=9 \ ft[/tex]. So, the area is
[tex]A=\frac{1}{2} (b \times h)[/tex]
[tex]A=\frac{1}{2}(7.8 \times 9) =35.1 \ ft^{2}[/tex]
Then, the total surface area of the pyramid is
[tex]S=4(35.1)=140.4 \ ft^{2}[/tex]
Therefore, the right answer is B. 140.4 square feet.
Emery's blueberry farm can produce 535 bushels of blueberries in 2 days. At this rate, how many bushels of blueberries can Emery's farm produce in 9 days? A. 2,675 B. 1,872.5 C. 2,140 D. 2,407.5
Answer: THE ANSWER IS D 2,407.5
Step-by-step explanation:
Use fraction operations to compare the regions of Canada in 5 different ways. Make sure that one comparison has 3 or more operations, one comparison involves 2 operations, and each of the four operations is used somewhere.
The fractions are Atlantic = 1/18
West = ¼
Territories = ⅓
Quebec = ⅙
Ontario = 1/9
Answer:
1/3,1/6,1/4
Step-by-step explanation:
atlantic and ontario do not compare
the others do
In ΔHIJ, i = 900 cm, ∠H=95° and ∠I=28°. Find the length of j, to the nearest centimeter.
Answer:
J=1607.77cm
Step-by-step explanation:
Answer:
1608
Step-by-step explanation:
a 20 in tall hexagonal pyramid has a regular hexagon base that can be divide into six equilateral triangles with side lengths of 12 in, as shown below find the area of the hexagon base rounded to the nearest hundredth
Answer:
c
Step-by-step explanation:
The area of hexagon base of hexagonal pyramid is option (A) 374.12 square inches.
What is a hexagonal pyramid?
A pyramid with a hexagonal base upon which are erected six isosceles triangular faces that meet at a point. All sides are equal, the angles between the sides are 120 degrees.
For the given situation,
The base of the hexagon, a = 12 in
The formula of the area of hexagon base is
[tex]A=\frac{3\sqrt{3}(a)^{2} }{2}[/tex]
On substituting the above values,
⇒ [tex]A=\frac{3\sqrt{3}(12)^{2} }{2}[/tex]
⇒ [tex]A=\frac{3\sqrt{3}(144 )}{2}[/tex]
⇒ [tex]A=374.12[/tex]
Hence we can conclude that the area of hexagon base of hexagonal pyramid is option (A) 374.12 square inches.
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A random sample of 850 births included 434 boys. Use a 0.10 significance level to test the claim that 51.5% of newborn babies are boys. Do the results support the belief that 51.5% of newborn babies are boys? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0: pequals0.515 Upper H 1: pnot equals0.515 Your answer is correct.B. Upper H 0: pequals0.515 Upper H 1: pgreater than0.515 C. Upper H 0: pnot equals0.515 Upper H 1: pequals0.515 D. Upper H 0: pequals0.515 Upper H 1: pless than0.515 Identify the test statistic for this hypothesis test.
The null hypothesis is that 51.5% of newborn babies are boys, and the alternative hypothesis is that the percentage is different from 51.5%. The test statistic, used to decide whether to reject or fail to reject the null hypothesis, is calculated using the observed percentage of boys and the sample size.
Explanation:The question is about testing a hypothesis about the proportion of boys born (51.5%). For this, we set our null and alternative hypotheses. The null hypothesis (H0) being tested here is that the true proportion of boys is 51.5% (p = 0.515), while the alternative hypothesis (H1) is that the proportion of boys is not 51.5% (p ≠ 0.515). The correct choice here would be A: Upper H0: p=0.515, Upper H1: p ≠ 0.515.
To calculate the test statistic, we would use the formula [(p' - p) / sqrt[(p(1 - p) / n]], where p' is the observed proportion in our sample (434 boys out of 850 births or 0.51), p is the claimed proportion (0.515), and n is the sample size (850). After calculating this, you would compare it to a critical value associated with the 0.10 significance level to decide whether to reject or fail to reject the null hypothesis.
Without the specific calculations, I can't tell you what your final test statistic will be, but this should guide you in the right direction.
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The null and alternative hypotheses are H₀: p = 0.515 and H₁: p ≠ 0.515. The test statistic for this hypothesis test is the z-score.
Explanation:The null and alternative hypotheses for this test are:
H₀: p = 0.515H₁: p ≠ 0.515The test statistic for this hypothesis test is the z-score. To calculate the z-score, you can use the formula:
z = (p' - p₀) / sqrt((p₀ * (1 - p₀)) / n)
Substituting the given values:
z = (434/850 - 0.515) / sqrt((0.515 * (1 - 0.515)) / 850)
Calculating the z-score, we can compare it to the critical value(s) from the standard normal distribution to make a conclusion about the null hypothesis.
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Which geometric series converges? 1 5 + 2 5 + 4 5 + 8 5 + 1 5 + 6 5 + 36 5 + 216 5 +... 1 5 +2+20+200+ 1 5 + 1 20 + 1 80 + 1 320 +.
Answer:
D. 1/5 + 1/20 + 1/80 + 1/320
Step-by-step explanation:
Edge
Option D.) 1/5 + 1/20 + 1/80 + 1/320 is correct
Geometric progression is kind of progression that the ratio to the adjacent values always same.
ratio in every option is not same except option D. 1/5 + 1/20 + 1/80 + 1/320
i.e. (1/5)/(1/20) = (1/80)/(1/20)
Thus the Option D.) 1/5 + 1/20 + 1/80 + 1/320 is correct
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6. The area of a rectangular painting is given by the trinomial x2 + 2x - 15. What are the possible (1 point)
dimensions of the painting? Use factoring,
Answer:
(x+5)(x-3) = x^2+2x-15
Step-by-step explanation:
since there is a -15 at the end and a +2x in the center, you want two factors of 15 which differ by 2. Those are 5 and 3. Now, you want one + and one -, so +5-3 = +2
Solve for x and y in the given the 45° - 45° - 90° triangle shown above. When applicable, simplify all radicals and show your work.
Answer:
x = 5.6 i guess
Step-by-step explanation:
use cos 45 = x/8
maybe
Solve the equation using the distributive property and properties of equality. -5(a + 3) = -55 What is the value of a? a 8 b -14 c 14 d -8
Answer:
It's C. 8
I took the edge test.
Answer:
C. 8
Step-by-step explanation:
Edge 2021
Leon runs 1 .6miles 5 day a week how many miles does he run in total in one week
Point O is on line RS. Find the
measure of angle SOP.
Solution:
Answer:
104°
Step-by-step explanation:
a straight line is 180°, so subtract angle ROP(76°) from it to get angle SOP
(Sorry forgot to put picture)
What is the value of x?
A. X=3
B. X=8.5
C. X=6.5
D. X=14
Also this one pls help
Answer:
Option 3
Step-by-step explanation:
Answer:
From my understanding the answer is supposed to be 6.. but since that's not an option I think it's option 4.
Step-by-step explanation:
an element with a mass of 540 grams decays by 17.9% per minute to the nearest tenth of a minute how long will it be until there are 90 grams of the element remainibg
Answer:
It'll take approximately 9.1 minutes
Step-by-step explanation:
The decay of this element can be modeled by the following expression:
m(t) = 540*(1 - 0.179)^t
Where m is the mass of the element in a given minute t. This expression comes from a compounded interest formula, with negative rate, since they will work in the same manner. Therefore to find how long until it reaches 90 g, we need to make m = 90 and solve for t.
90 = 540*(0.821)^t
(0.821)^t = 90 / 540
(0.821)^t = 1/6
ln(0.821^t) = ln(1/6)
t*ln(0.821) = ln(1) - ln(6)
t*ln(0.821) = - ln(6)
t = -ln(6)/ln(0.821) = 9.08452
It'll take approximately 9.1 minutes
Answer:the correct answer is 9
Step-by-step explanation:
hi guys could you please help me with this problem?
Answer:
7
Step-by-step explanation:
yidtkddkyoufofytidtsitdydiyof
Who knows the correct answer to this???
Answer:
A. y = 3x + 1
Step-by-step explanation:
Slope-intercept form y = mx + b
m = slope
b = y - intercept
please help me and please help me do it in a way i could understand :) ty
Suppose you purchase a $500 bond with a 6.5% coupon. What is the periodic
interest rate of this bond?
O A. 6.5%
O B. 0.5%
O C. 3.25%
O D. 1.5%
Answer:
C. 3.25
Step-by-step explanation:
A was wrong I seen the real answer which was C
Willy has compounded monthly to invest his summer earnings of $4259 in the
Rock Solid Bank. The bank is offering 6%. Willy plans to use the money to go to
college in 5 years. How much will he have in 5 years?
We have been given that Willy has compounded monthly to invest his summer earnings of $4259 in the Rock Solid Bank. The bank is offering 6%. We are asked to find the amount of money will be after 5 years.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
t = Time in years.
[tex]6\%=\frac{6}{100}=0.06[/tex]
Since interest is compounded monthly, so [tex]n=12[/tex] and [tex]P=4259[/tex].
[tex]A=\$4259(1+\frac{0.06}{12})^{12\cdot 5}[/tex]
[tex]A=\$4259(1+0.005)^{60}[/tex]
[tex]A=\$4259(1.005)^{60}[/tex]
[tex]A=\$4259(1.3488501525493161)[/tex]
[tex]A=\$5744.752799707\approx \$5744.75[/tex]
Therefore, Will will have approximately [tex]\$5744.75[/tex] in 5 years.
Use the net as an aid to compute the surface area (rounded to the nearest integer) of the triangular pyramid with an equilateral triangle base.
A) 130 yd2
B) 150 yd2
C) 170 yd2
D) 190 yd2
1. How long is a whales head?
its 1/3 of the length of its body
Answer:
Whales head
Step-by-step explanation:
1/3
In the figure, AC = 15 ft, m∠ABC = 60°, m∠ADC = 45°, and m∠AEC = 30°. Find each of the following measures. Show your work or explain your reasoning.
Answer:
a) BC = 8.66 feet
b) AD = 21.2134 feet
c) EC = 25.9785 feet
Step-by-step explanation:
a)
To find the length of BC, we just need to use the tangent relation of the angle ABC, where the opposite side is the length of AC and the adjacent side is the length of BC:
tangent(60) = AC / BC
1.7321 = 15 / BC
BC = 15 / 1.7321 = 8.66 feet
b)
To find the length of AD, we just need to use the sine relation of the angle ADC, where the opposite side is the length of AC and the hypotenusa is the length of AD:
sine(45) = AC / AD
0.7071 = 15 / AD
AD = 15 / 0.7071 = 21.2134 feet
c)
Similarly to the procedure in letter a), to find the length of EC, we just need to use the tangent relation of the angle AEC, where the opposite side is the length of AC and the adjacent side is the length of EC:
tangent(30) = AC / EC
0.5774 = 15 / EC
EC = 15 / 0.5774 = 25.9785 feet
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation.
Answer:
x = sine 70° / 8
Step-by-step explanation:
write an expression that represents "the product of 12 and n"
Answer:
12n
Step-by-step explanation:
12 * n= 12n
Answer:
12n
Step-by-step explanation:
You don't really need to do anything it's as simple as it can be!
What is the distance between the point (-25, 10) and the origin?
Answer:
35
Step-by-step explanation:
The origin is (0,0). To get to it from (-25,10) you would add 25 which would get you to (0,10,). Then you subtract 10 to get you to the origin. 10+25=35
For a normal distribution given a standard deviation of 3.8 in a mean of 54 what percent lies above 48
A 0.1690
B 0.0571
C 0.7660
D 0.9429
Answer:
choice D.) 0.9429
Step-by-step explanation:
Given a Normal data set
mean u = 54
standard deviation s = 3.8
we want P( X > 48)
Standardize this probability so we can use Z-scores.
P( X > 48) = P( (X - u)/s > (48 - 54)/3.8 ) = P(Z > -1.5789)
so I look for P ( Z > 1.5789) = 0.0571
so P(Z > -1.5789) = 1 - P(Z > 1.5789) = 1 - 0.0571 = 0.9429
if a circle has a circumference of 100 pi units what is its area
Step-by-step explanation:
We have,
Circumference of a circle is 100 π.
Formula for circumference is :
[tex]C=2\pi r[/tex]
r is radius of circle
[tex]r=\dfrac{C}{2\pi}\\\\r=\dfrac{100\pi }{2\pi}\\\\r=50\ \text{units}[/tex]
Formula for area of circle is :
[tex]A=\pi r^2\\\\A=\pi (50)^2\\A=2500\pi\ \text{units}^2[/tex]
the area of the circle is 2500π square units.
To find the area of a circle when given the circumference, we must first determine the radius of the circle. The formula for the circumference of a circle is C = 2 π r, where C is the circumference and r is the radius. In this case, the circumference is 100 π units.
We can solve for the radius (r) as follows:C = 2 π r100 π = 2 π rr = 100 π / (2 π)r = 50 unitsSubstitute the radius (50 units) into the area formula:
A = π * (50 units)²A = π * 2500 units²A = 2500 π units²Amanda delivers 56 meals in 4 hours. At this rate, how many meals can she deliver is 7 hours?
Answer:
98
Step-by-step explanation:
On average she delivers about 14 meals per hour
If you divide 56 by 4 you get 14 ^
Then if you multiply 14 by 7 you get 98