Bill is building a staircase for his new home. He has measured several three-foot bars to support the handrail. If Bill nails the support bars to the handrail and to the edge of the staircase (a 2-inch-by-12-inch board attached parallel to the slope of the stairs) at 12-inch intervals, will the handrail be parallel to the staircase?

Answer:

t=3.5 seconds

Step-by-step explanation:

Given

h(t) = −16t^2 + 111t + 0

h'(t)= -32t + 111

Maximum height occurs when h(t) = 0 and the ball begins to fall

h(t)= -32t + 111=0

-32t + 111=0

-32t=-111

Divide both sides by -32

t=3.46872

Approximately, t=3.5 seconds

Recall,

Maximum height occurs when h(t) = 0

h(t)= -32t + 111=0

= -32(3.46872)+111

= -110.99904+111

= 0.00096 ft

Answer:

The ratio of their surface areas would 1:9 and the ratio of their volumes would be 1:27

Step-by-step explanation:

Given Info: The sides of two cubes are in ratio of 1:3. We can assign one square x and the other square 3x.

We know that the area of a square is its side squared, and that a cube has 6 sides. So thus if we assign one side of the cube x we can assume that surface area is 6x^2:

Surface Area of Cube #1= 6x^2

Surface Area of Cube #2= 6((3x)^2) = 6(9x^2) = 54x^2

Ratio of Surface Area: 6x^2 : 54x^2 = 6:54 = 1:9

Now for the volume we know that it is equivalent to one side cubed. So after assigning x to one cube, we can assume that volume would be x^3.

Volume of Cube #1= x^3

Volume of Cube #2= (3x)^3 = 27x^3

Ratio of Volume: x^3: 27x^3 = 1:27

Hope this helps!

Answer:

The square root of 38.

Step-by-step explanation:

The square root of 38 is about 6.16.

The square root of 35 is about 5.91.

The square root of 45 is about 6.70.

The square root of 48 is about 6.92,

So the most reasonable one is the square root of 38, since it is much closer to 6.

Answer:

k = 45

Step-by-step explanation:

We can put this into an equation form:

k - 10 = 35

We can solve for k by adding 10 to both sides:

k = 45

Answer:

k-10=35

k=45

Step-by-step explanation:

Let's write this as an equation.

"10 less than k" means subtract 10 from k.

k-10

"is 35" means equals 35.

k-10=35

If we want to solve for k, we have to get k by itself on one side of the equation.

k-10=35

10 is being subtracted from k. The inverse of subtraction is addition. Add 10 to both sides of the equation.

k-10+10=35+10

k=35+10

k=45

Answer:

180

Step-by-step explanation:

This is becuase 4*5*9 is equal to 180, to find the total number of combinations, you multiply how many of each there are.

Answer:

5/6w=2/3

5/6(4/5)=2/3

20/30=2/3

20/30=10/15=2/3=2/3

Proof:

5/6w=2/3

6/5*5/6w=2/3*6/5

30/30w=2/3*6/5

w=12/15=4/5

Hope this helps ;) ❤❤❤

Answer:

cos theta = √8/3

tan theta = √8/8

Step-by-step explanation:

sin theta = 1/3

1² + x² = 3²

x = √8

cos theta = √8/3

tan theta = 1/√8 = √8/8

Answer:

Step-by-step explanation:

The formula you need to solve for angle x is:

∠x = 1/2(large arc - small arc)

We have enough info to find what we need to solve for the arcs. 58° is an inscribed angle. The rays of the angle cut off an arc on the circle and that arc measure is twice the measure of the angle. So the smaller arc is 58 * 2 = 116. Since around the outside of the circle measures 360°, then the larger arc measures 360 - 116 = 244. So the larger arc is 244. Filling in the formula to solve for the angle x:

∠x = 1/2(244 - 116) and

∠x = 1/2(128) so

∠x = 64

D is your answer.

Answer:

D.) 64

Step-by-step explanation:

I got it correct on founders edtell

Answer:

0.0425

Step-by-step explanation:

probability of  basket player = 0.25

probability of being a soccer player = 0.17

chances that a sixth grader plays basketball AND soccer = 0.25×0.17 = 0.0425

Answer:

a. The coordinates of the first train are (-12,6).  The coordinates of the second train are (20,35).

b. The slope of the line for the first train is [tex]-\frac{1}{2}[/tex].  The slope is neither horizontal or vertical.  It slopes diagonally downward from left to write since the slope is negative.  In slope-interdept form, it is written as [tex]y=-\frac{1}{2} x[/tex].  In standard form, it is written as [tex]x+2y=0[/tex].   The slope of the line for the second train is [tex]\frac{7}{4}[/tex].  The slope is neither vertical or horizontal.  It slopes diagonally upward from left to right since the slope is positive.  In slope-intercept form, it is written as [tex]y=\frac{7}{4}x[/tex].  In standard form, it is written as [tex]-7x+4y=0[/tex].

c. The equarion of a line in slope-intercept form of the new track would be [tex]y=-\frac{1}{2} x+2[/tex].

Step-by-step explanation:

a.  The way to find the coordinates is either to picture a coordinate grid in your head or to have one out in front of you for a visual.  The first train travels 12 miles west, or 12 units to the left (-12), and 6 miles north, or 6 units up (6).  On a coordinate plane, that would be marked as (-12,6).  The second train travels 20 miles east, or 20 units to the right (20), and 35 miles north, or 35 units up (35).  On a coordinate plane that would be marked as (20,35).  This means that the coordinates of the first train would be (-12,6), and the coordinates of there second train would be (20,35).

b. The way to find slope is to find [tex]\frac{delta "x"}{delta "y"}[/tex].  "Delta" means "the change in".  The equation would be [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].  So, let's find the slope of the first train's travel path.  We'll use the origin, (0,0), and the stopping point, (-12,6), as our coordinates to find the slope.  [tex]\frac{0-6}{0-(-12)}=\frac{0-6}{0+12}=\frac{-6}{12}=\frac{-1}{2}=-\frac{1}{2}[/tex].  That makes the slope of the first train's travel path to be (-1/2).  Now, let's find the slope of the second train's travel path.  We'll use the origin, (0,0), and the stopping point, (20,35), as our coordinates to find the slope.  [tex]\frac{0-35}{0-20}=\frac{-35}{-20}=\frac{35}{20}=\frac{7}{4}[/tex].  That makes the slope of the second train's travel path to be (7/4).  They want to know the equation of the travel path line in slope-intercept form and in standard form, and what the line looks like.  To start off, any vertical line would be undefined, and that would be if the slope was a fraction with a denominator of zero, which doesn't occur for either train path.  A horizontal line  would be if the slope was zero itself and the trains were not moving, but the trains are moving, so that's not possible either.  The way to determine theway a slope is diagonally is to look at whether the slope is positive or negative.  The first train's path slopes negatively, so it moves diagonally downward from left to right, or diagonally upward from right to left (both the same thing).  The second train's path slopes positively, so it moves diagonally upward from left to right, or diagonally downward from right to left.  Finally, the equations for this part of the question.  For both trains, the origin is the y-intercept, so the y-intercept does not have to be written in the slope-intercept equation.  The slope-intercept form of an equation of a line is [tex]y=mx+b[/tex] where "m" is the slope and "b" is the y-intercept.  The "b" value is 0, so that will not be written.  The slope for the first train is (-1/2), so the slope-intercept form of the first train's travel path is y=(-1/2)x.  The slope of the second train is (7/4), so the slope-intercept form for this train's path is y=(7/4)x.  As for standard form, subtract the "mx" value from both sides, and set the equation equal to 0. Also, get rid of any fractions. So, for the first train, standard form would be x+2y=0.  And for the second train, standard form would be -7x+4y=0.

c.  Parallel means having the same slope but a different y-intercept.  The second train station would be placed two miles north, or two units up, from the first train station.  The first train station is at (0,0), so the second train station would be placed at (0,2).  That makes 2 the y-intercept for if the first train had taken the second train station's travel route.  The slope for the intitial route was (-1/2), so that will stay the same.  Therefore, the equation of thr route taken if the first train had come out of the second train station, if it was already built, would be y=(-1/2x)+2.

Answer: It is a Rotation Angle 90 Degrees clockwise about the point (3,4)

Step-by-step explanation:

Mark the point (3,4) with your finger and turn your phone once to the right Your old shape is where your new shape your be now. That’s rotation.

Answer:

Value of x is 8

Step-by-step explanation:

Given:

[tex]\sqrt{\frac{896z^{15}}{225z^6} }=\frac{xz^4}{15} \sqrt{14z}\\\\Computation: \\\\From\ squaring\ both\ side\\\\ {\frac{896z^{15}}{225z^6} }=\frac{x^2z^8}{225} ({14z})\\\\896z^9=14x^2z^9\\\\896=14x^2\\\\64=x^2\\\\x = 8[/tex]

So, Value of x is 8

Answer: 14 units^2

Step-by-step explanation: 2 times 3 is 6, 2 times 4 is 8, 6+8=14.

Answer:

Option (2)

Step-by-step explanation:

In the given circle,

[tex]m(\widehat{CBD})+m(\widehat{CED})[/tex] = 360°

Therefore, 212° + [tex]m(\widehat{CED})[/tex] = 360°

[tex]m(\widehat{CED})=360-212[/tex]

               = 148°

Tangent - chord theorem states,

"Angle between a chord and tangent measure the half of the angle measure of the intercepted minor arc."

m∠ACD = [tex]\frac{1}{2}(\widehat{CED})[/tex]

              = [tex]\frac{1}{2}(148)[/tex]  

              = 74°

Therefore, measure of ∠ACD is half the measure of arc CD or 74°.

Option (2) will be the correct option.

Answer:

NOT a rational expression.

Step-by-step explanation:

A rational expression is a fraction of two polynomials.

Since the denominator contains a square-root radical, it is not considered a polynomial.

Therefore the given exprssion is NOT a rational expression.

Answer:

The correct option is;

C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1

Please find attached the required function graph

Step-by-step explanation:

To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;

x [tex]{}[/tex]       F(x)

-4[tex]{}[/tex]       30

-3[tex]{}[/tex]       0

-2[tex]{}[/tex]       6

-1[tex]{}[/tex]        0

0 [tex]{}[/tex]      -18

1[tex]{}[/tex]         0

2[tex]{}[/tex]       150

The shape of a graph with multiplicity of 2

Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;

x = 1, -1, and, giving

(x - 1)·(x + 1)·(x - 3)² = 0

Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.

Answer:

C

Step-by-step explanation:

Answer:

Domain : [-2, 6], {x | -2 ≤ x ≤ 6}

Range : [-6, 2], {y | -6 ≤ y ≤ 2 }

Step-by-step explanation:

Domain of a function is defined by the x-values on the graph of the function.

Similarly, y-values define the Range of the function.

From the graph of a circle,

Diameter of the circle along x-axis (horizontally) has the ends at x = -2 and x = 6

Therefore, domain of the circle will be [-2, 6], {x | -2 ≤ x ≤ 6}

Extreme ends of the diameter of the circle along y-axis are at y = 2 and y = -6

Therefore, range of the circle will be [-6, 2], {y | -6 ≤ y ≤ 2 }

Answer:

275 miles

Step-by-step explanation:

I assume all towns are on the same line. Then, town C is 5.5 cm from town A on the map since 3.5 cm + 2 cm = 5.5 cm.

The real distance can be calculated with a proportion.

2/100 = 5.5/x

2x = 5.5 * 100

2x = 550

x = 275

Answer: 275 miles

Answer:

V = 125 cu.

Step-by-step explanation:

Since volume = L x W x H -->

Plug the numbers in --> 5 x 5 x 5 (5 cubed) -->

25 x 5 = 125

Thus, the total volume of this cube is 125 cu.

Hope this helps!

Answer:

Step-by-step explanation:

Volume of a cube = l³

where l is the length of one side

From the question

there are 5 squares on each side of the cube

So l = 5 units

Volume of the cube = 5³

We have the final answer as

Hope this helps you

Answer:

second table

Step-by-step explanation:

Out of the 8 options on the spinner, 2 of them are 0's, 1 of them is a 1, 2 of them are 2's and 3 of them are 3's so the probability of spinning a 0, 1, 2 or 3 is 2/8, 1/8, 2/8 or 3/8 which becomes 0.25, 0.125, 0.25 or 0.375 respectively. Therefore, the answer is the second table.

Answer:

See below.

Step-by-step explanation:

Approximation:

The wall is 8 ft wide.

The frame is 22 1/4 inches wide. 22 1/4 inches is close to 2 ft since 2 ft = 24 inches.

8 ft - 2 ft = 6 ft

There will be approximately 6 ft of space tot he sides of the frame.

6 ft/2 = 3 ft

3 ft * 12 in./ft = 36 in.

There will be approximately 36 in. on each side of the frame.

Exact:

8 ft - 22 1/4 in. = 8 * 12 in. - 22 1/4 in. =

= 96 in. - 22 1/4 in.

= 95 4/4 in. - 22 1/4 in.

= 73 3/4 in.

The total amount of width of the wall not occupied by the frame is 73 3/4 in.

Half of that amount is on each side of the frame.

(73 3/4 in.)/2 = (73 3/4 in.) * 1/2 = (73 * 1/2 + 3/4 * 1/2) in. =

= 36 1/2 in. + 3/8 in.

= 36 4/8 in. + 3/8 in.

= 36 + 7/8 in.

= 36 7/8 in.

Answer:

Chemistry

Step-by-step explanation:

To solve the above question, we use the z score formula

Andy took two Exams, Chemistry and Spanish. So we find the z score for both exams.

a) Chemistry Exam

On the chemistry exam, the mean was µ = 30 with σ = 5, and Andi had a score of X = 45

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

z = (45 - 30)/5

z = 15/5

z = 3

b) On the Spanish exam, the mean was µ = 60 with σ = 6 and Andi had a score of X = 65.

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z = (x-μ)/σ

z = (65 - 60)/6

z = 5/6

z = 0.8333333333

Comparing the z score of both Exams,

Andy had a z score of 3 in the Chemistry exam and 0.8333333333 in the Spanish exam.

Therefore, Andy should be expecting a better grade in the Chemistry exam because his z score in the Chemistry exam was higher than that of the Spanish exam.

Answer:

-8.05

Step-by-step explanation:

In order to solve for C you first have to subtract 17.6 from both sides.

2c=(6/4)-17.6

6/4 is 1.5

1.5-17.6=-16.1

2c=-16.1

c=-8.05

Answer:

1.5

Step-by-step explanation:

2c+17.6=6/4

2c+176/10=6/4

2c+88/5=6/4

2c=6/4-88/5

2c=30-352/20

2c=-322/20

2c=-161/10

c=-8.05

Proof:

2c+17.6=6/4

2(-8.05)+17.6=6/4

-16.1+17.6=6/4

1.5=1.5

Hope this helps ;) ❤❤❤

Answer:

The correct option is a.

Step-by-step explanation:

The standard deviation of the sampling distribution of sample mean ([tex]\bar x[/tex]) is known as the standard error. It is denoted by [tex]\sigma_{m}[/tex].

The formula to compute the standard error is:

[tex]\sigma_{m}=\frac{\sigma}{\sqrt{n}}[/tex]

As the population standard deviation is divided by the square root of the sample size, the standard error can never be more than the population standard deviation, σ.

Also, since the population standard deviation is directly proportional to the standard error, the value of [tex]\sigma_{m}[/tex] is affected by the value of σ.

And since the sample size is inversely proportional to the standard error, the value of [tex]\sigma_{m}[/tex] decreases as the value of n increases.

The sample mean is a statistic, i.e. it represents a specific characteristic (here, the average) of the sample.

The standard deviation of any statistic measures the variability of the statistic.

So, the standard error measures the variability in sample means.

Thus, the correct option is a.

Answer:

4

Step-by-step explanation:

4x4x4=64

Answer:

0.4193

Step-by-step explanation:

Root 64=8

Root 364=19.08...in 4 s.f

8÷19.08=0.4193...in 4 significant figures (4s.f)

Answer:

3(a). The ship travelled in north is 26.0 km.

(b). The ship travelled in east is 23.4 km.

4(a). The ship travelled in south is -88.61 km.

(b). The ship travelled in west is -179.29 km.

Step-by-step explanation:

Given that,

(3). Distance = 35 km

Angle = 42°

Let distance in north is y km.

We need to calculate the distance

Using vertical component

[tex]y = d\cos\theta[/tex]

Put the value into the formula

[tex]y = 35\cos42[/tex]

[tex]y=26.0\ km[/tex]

Let distance in east is x  km

We need to calculate the distance

Using horizontal component

[tex]x =d\sin\theta[/tex]

Put the value into the formula

[tex]x = 35\sin42[/tex]

[tex]x=23.4\ km[/tex]

(4). A ship sails 200 km on a bearing of 243.7°

Let distance in south is y km.

We need to calculate the distance

Using vertical component

[tex]y = d\cos\theta[/tex]

Put the value into the formula

[tex]y = 200\cos243.7[/tex]

[tex]y=-88.61\ km[/tex]

Let distance in west is x  km

We need to calculate the distance

Using horizontal component

[tex]x =d\sin\theta[/tex]

Put the value into the formula

[tex]x = 200\sin243.7[/tex]

[tex]x=-179.29\ km[/tex]

Hence, 3(a). The ship travelled in north is 26.0 km.

(b). The ship travelled in east is 23.4 km.

4(a). The ship travelled in south is -88.61 km.

(b). The ship travelled in west is -179.29 km.

Answer:

0.32 grams

Step-by-step explanation:

ratio of weight of -copper, zinc, manganese, and nickel = 177:12:7:4

let the

weight of copper = 177x

weight of zinc = 12x

weight of manganese = 7x

weight of nickel = 4x

Total weight of this alloy in terms of x =  177x + 12x+ 7x + 4x = 300x

given weight of alloy = 8 grams

thus,

weight of this alloy in terms of x =given weight of alloy

300x = 8 grams

x = 8/300 grams =

weight of zinc = 12x = 12 * 8/300 grams = 96/300 grams = 0.32 grams

Because 9 × 10 equals 90

Then 7×90=7×9×10

Answer:

It does not matter which color you add first because either way you will end up with the same color, purple. We can relate this to the commutative property of addition because blue + red = red + blue.

Pls mark it Brainliest!!!

[tex]6x^2+12x=5x-2\\6x^2+7x+2=0\\6x^2+3x+4x+2=0\\3x(2x+1)+2(2x+1)=0\\(3x+2)(2x+1)=0\\x=-\dfrac{2}{3} \vee x=-\dfrac{1}{2}[/tex]