Step-by-step explanation:
We have (x + y)² = (x + y)(x + y) = x² + 2xy + y².
Let x be 3a and y be 2.5b.
Therefore (3a + 2.5b)²
= (3a)² + 2(3a)(2.5b) + (2.5b)²
= 9a² + 15ab + 6.25b².
Hence the '*' sign should be replaced with 15ab.
Answer:
Given that, ( 3a + 2.5b )² = 9a² + 6.25b² + *
We know that, ( x + y )² = x² + y² + 2xy
According to the above problem, we get
( 3a + 2.5b )² = (3a)² + (2.5b)² + (2×3a×2.5b)
( 3a + 2.5b )² = 9a² + 6.25b² + 15ab
Therefore,
The sign " * " should be 15ab.
15ab is the right answer.What is the mass percent of cashews in a 10. 0g mixed nut sample if the cashews are 0. 87g?
Answer:
0.87%
Step-by-step explanation:
→ Divide 0.87 by 10
0.87 ÷ 100 = 0.0087
→ Multiply answer by 100
0.0087 × 100 = 0.87
15 POINTS!!!! PLS HELP LOOK AT PIC
Answer:
A
Step-by-step explanation:
The solutions of a quadratic function will always be the x intercepts. Thus, if there are two solutions, there are two x intercepts.
If a polynomial f(x) is divided by (x+a) and leaves the reminder is a and b are constants then
f(-a) is the remainder when f(x) is divided by (x+a). This can be obtained by remainder theorem for polynomials.
What is the required remainder?Given that f(x) is divided by (x+a) and leaves a reminder
Using the remainder theorem for polynomials we get,
f(x) = (x+a)·g(x) + r, where g(x) is the quotient and r is the remainder.
Put x = -a, then
f(-a) = (-a+a)·g(-a) + r
f(-a) = (0)·g(x) + r
f(-a) = r
f(-a) is the remainder.
Hence f(-a) is the remainder when f(x) is divided by (x+a).
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uan recently hired a roofer to do some necessary work. On the final bill, Juan was charged a total of $1131.5. $450 was listed for parts and the rest for labor. If the hourly rate for labor was $47, how many hours of labor was needed to complete the job?
Based on the total cost that Juan incurred to hire the roofer including the charge for parts and labor, the number of hours that was needed to complete the job was 14.50 hours.
How many hours did the roofer use?The first thing to do is to find out the amount that went to labor:
= Final bill - cost of materials
= 1,131.5 - 450
= $681.50
Now that you have the cost of labor, you can find out the number of labor hours that were used based on the hourly rate:
= Cost of labor / Hourly rate
Solving gives:
= 681.50 / 47
= 14.5 hours
In conclusion, the number of labor hours that the roofer used to complete the work, based on the total amount charged to Juan is 14.50 hours.
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I need help on this please!
Answer:
Step-by-step explanation:
Part A:
CIRCLE A : Circumference is (pi)(diameter) so if they give you the circumference (21.98), divide it by 7 which gives you 3.14.
CIRCLE B: 18.84/6 = 3.14
Part B:
CIRCLE A: Area is (pi)(radius^2) so if they give you the area (38.465), divide it by radius^2 (7/2 = 3.5^2 = 12.25) = 3.14
CIRCLE B: 28.26/(3^2) = 3.14
Part C:
The value of pi stays the same for circle A and B.
Hope this helps :)
( will give brainlyest)
A firework is launched from the ground at a speed of 160 feet per second. It’s height after t seconds is given by the polynomial -16t+160t. What is the height of the firework after 4 seconds?
Answer: 384 feet
Step-by-step explanation:
We will simplify and solve -16t² + 160t when t is equal to 4.
-16t² + 160t
-16(4)² + 160(4)
384 feet
Answer:
Step-by-step explanation:
**Note: The polynomial in question is -16t² + 160t, as clarified in the discussion under the question.**
Since there is a polynomial to find the height given a certain time, the height is a function of time.
This function would be h(t) = -16t² + 160t, so plugging in 4 for t would give the height.
[tex]h(4) = -16(4)^2+160(4)[/tex]
[tex]-16(16)+160(4)[/tex] [Squaring 4]
[tex]-256 + 640[/tex] [Multiplying]
[tex]384[/tex] [Combining both terms]
Hence, the height of the firework after 4 seconds is 384 feet.
Please help quickly I need the answer now please you’ll be brainleist
Answer:
B
Step-by-step explanation:
See the attached image.
22 A circle passes through the points
P(3, 0) and Q(0, 5). Its centre lies on
the line y = x + 2.
(i) Find the equation of the perpendicular bisector of PQ.
(ii) Hence show that the coordinates of the centre of the circle are (-1, 1).
(iii) Find the equation of the circle.
A second circle with equation
2x² + y² + ax + by - 14 = 0 has the
same centre as the first circle.
(iv) Write down the value of a and of b.
(v) Show that the second circle lies
inside the first circle.
The equation of the first circle is (x + 1)^2 + (y - 1)^2 = r^2 and the equation of the second circle is (x + 1)² + (y - 1)² = 16
The equation of the perpendicular bisectorThe points are given as:
P(3, 0) and Q(0, 5)
The midpoint of PQ is
Midpoint = 0.5(3 + 0, 0 + 5)
Midpoint = (1.5, 2.5)
Calculate the slope of PQ
m = (y2 - y1)/(x2 - x1)
m = (5 - 0)/(0 - 3)
m = -5/3
A line perpendicular to PQ would have a slope (n) of
n = -1/m
This gives
n = -1/(-5/3)
n = 0.6
The equation is then calculated as:
y = n(x - x1) + y1
Where
(x1, y1) = (1.5, 2.5)
So, we have:
y = 0.6(x - 1.5) + 2.5
y = 0.6x - 0.9 + 2.5
Evaluate the sum
y = 0.6x + 1.6
Hence, the equation of the perpendicular bisector of PQ is y = 0.6x + 1.6
The center of the circleWe have:
y = x + 2
Substitute y = x + 2 in y = 0.6x + 1.6
x + 2 = 0.6x + 1.6
Evaluate the like terms
0.4x = -0.4
Divide
x = -1
Substitute x = -1 in y = x + 2
y = -1 + 2
y = 1
Hence, the center of the circle is (-1, 1)
The circle equationWe have:
Center, (a, b) = (-1, 1)
Point, (x, y) = (0, 5) and (3, 0)
A circle equation is represented as:
(x - a)^2 + (y - b)^2 = r^2
Where r represents the radius.
Substitute (a, b) = (-1, 1) in (x - a)^2 + (y - b)^2 = r^2
(x + 1)^2 + (y - 1)^2 = r^2
Substitute (x, y) = (0, 5) in (x + 1)^2 + (y - 1)^2 = r^2
(0 + 1)^2 + (5 - 1)^2 = r^2
This gives
r^2 = 17
Substitute r^2 = 17 in (x + 1)^2 + (y - 1)^2 = r^2
(x + 1)^2 + (y - 1)^2 = r^2
Hence, the circle equation is (x + 1)^2 + (y - 1)^2 = r^2
The value of a and bThe equation of the second circle is
2x² + y² + ax + by - 14 = 0
Rewrite as:
2x² + ax + y² + by = 14
For x and y, we use the following assumptions
2x² + ax = 0 and y² + by = 0
Divide through by 2
x² + 0.5ax = 0 and y² + by = 0
Take the coefficients of x and y
k = 0.5a k = b
Divide by 2
k/2 = 0.25a k/2 = 0.5b
Square both sides
(k/2)² = 0.0625a² (k/2)² = 0.25b²
Add the above to both sides of the equations
x² + 0.5ax +0.0625a² = 0.0625a² and y² + by + 0.25b² = 0.25b²
Express as perfect squares
(x + 0.25a)² = 0.0625a² and (y + 0.5b)² = 0.25b²
Add both equations
(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²
So, we have:
2x² + ax + y² + by = 14 becomes
(x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14
Comparing the above equation and (x + 1)^2 + (y - 1)^2 = r^2, we have:
0.25a = 1 and 0.5b = -1
Solve for a
a = 4 and b = -2
This means that the value of a is 4 and b is -2
Show that the second circle is in the firstWe have:
a = 4 and b = -2
Substitute these values in (x + 0.25a)² + (y + 0.5b)² = 0.0625a² + 0.25b²+ 14
This gives
(x + 0.25*4)² + (y - 0.5*2)² = 0.0625*4² + 0.25*(-2)²+ 14
(x + 1)² + (y - 1)² = 16
The equation of the first circle is
(x + 1)² + (y - 1)² = 17
The radii of the first and the second circles are
R = √17
r = √16
√17 is greater than √16
Since they have the same center, and the radius of the first circle exceeds the radius of the second circle, then the second circle lies inside the first circle.
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Given the right triangle below, for the Pythagorean theorem, in which a 2 + b 2 = c 2, which side would represent the side "c." Hint: look at this triangle and the names of the angles.
Answer:
line segment AC (hypotenuse)
Step-by-step explanation:
The Pythagorean Theorem states that the sum of squares of the base/height of the triangle will equal the hypotenuse squared which is what c is equal to. So the c would represent the hypotenuse which is the side from the points A to C in the diagram.
How many miles is it across the united states from the east coast to the west coast.
The thousand of miles across the United states from the east coast to the west coast.
In order to find the number of miles across the United states from the east coast to the west coast.
Hence, the thousand of miles across the United states from the east coast to the west coast.
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Calculate the total amount in an investment account if $2800 was invested at a simple interest rate of
5.5% for 18 months.
a. $3034.15
b. $3031.00
Trinh invected $2400.st.0866
c. $7340.11
d.
$5544.00
The total amount in the investment account is $3031.00
How to determine the total amount?The given parameters are
Principal, P = $2800
Rate, r = 5.5%
Time = 18 months i.e. 1.5 years
The amount is then calculated as:
A = P + PRT
This gives
A = 2800 + 2800 * 5.5% * 1.5
Evaluate
A = 3031
Hence, the total amount in the investment account is $3031.00
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3) A normal distribution has a mean of 75 and a standard deviation of 15. Determine the z-score for the data value of 85.
Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (85 - 75)/15 = 10/15 = 2/3 = 0.666666... ≈ 0.67
as z-tables usually round the z-score to hundredths.
The z-score for the data value of 85 is 0.67.
How to Calculate Z-Score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score. A value that is one standard deviation from the mean would have a Z-score of 1.0. Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean.
To find the z-score, you simply need to apply the following formula:
z = (x - μ) / σ
μ=75
σ=15
x=85
z =85-75/15
z=10/15
=2/3
=0,66666....=0.67
Therefore, the z-score for the data value of 85 is 0.67.
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A bookstore sells books for $2, $3, $5, and $10. Let random variable X = "amount of
money for one book."
Look at the relative-frequency table below representing the amount of money spent on
one item and the relative frequencies with which customers purchase them
If the expected amount of money spent by a customer is $3.23 what is the standard deviation?
The value of the standard deviation is σ = 2.20. Using probability distribution, the required standard deviation is calculated.
How to calculate the standard deviation?The formula for the standard deviation of the given probability distribution is
σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²
Where the mean μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]
Calculation:It is given that,
x: $2, $3, $5, $10
P(X=x): 0.55, 0.26, 0.11, 0.08
Step 1: Calculating the mean:
we have μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]
⇒ μₓ = 2 × 0.55 + 3 × 0.26 + 5 × 0.11 + 10 × 0.08
∴ μₓ = 3.23
Step 2: Calculating the standard deviation:
x: 2, 3, 5, 10
x²: 4, 9, 25, 100
P(X=x): 0.55, 0.26, 0.11, 0.08
([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]: 4 × 0.55 = 2.2; 9 × 0.26 = 2.34; 25 × 0.11 = 2.75; 100 × 0.08 =8
∑[([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]]: 2.2 + 2.34 + 2.75 + 8 = 15.29
Therefore,
The standard deviation, σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²
⇒ σ = [tex]\sqrt{15.29-(3.23)^2}[/tex]
= [tex]\sqrt{15.29-10.43}[/tex]
∴ σ = 2.20
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What is the surface area of the right cone below?
A. 63π units²
B. 54π units ²
C. 99π units²
D. 126π units²
Answer:
B. 54π units ²
Step-by-step explanation:
solution:
given,
Radius (r) = 3
(l) = 15
we know that,
T.S.A. of cone = πr( r + l )
= π × 3(3 + 15)
= π × 3 × 18
= π × 54
= 54π units ²
Which expression is equivalent to (m-4/m+4)/(m+2)?
A) m-4/(m+4)(m+2)
B) (m+4)(m+2)/m-4
C) (m-4)(m+2)/m+4
D) m+4/(m-4)(m+2)
Hello,
[tex] \frac{ \frac{m - 4}{m + 4} }{m + 2} = \frac{ \frac{m - 4}{m + 4} }{ \frac{m + 2}{1} } = \frac{m - 4}{m + 4} \times \frac{1}{m + 2} = \frac{m - 4}{(m + 4)(m + 2)} [/tex]
What is the slope of the line containing (-3, 1) and (1, -2)?
[tex]\textbf{Heya !}[/tex]
use the slope-formula:-
[tex]\sf{\cfrac{y2-y1}{x2-x1}}[/tex]
put-in the values
[tex]\sf{\cfrac{-2-1}{1-(-3)}}[/tex]
[tex]\sf{\cfrac{-3}{1+3}}[/tex]
[tex]\sf{\cfrac{-3}{4}[/tex]
[tex]\sf{-\cfrac{3}{4}}[/tex]
`hope it's helpful to u ~
Solve for X in the diagram below
Step-by-step explanation:
the sum of all angles around a single point on one side of a line must be 180°.
because that line can be seen as the extension of the diameter of a circle, and the point would be the center of that circle. so, one side of the line represents a half-circle, which stands for 180°.
so we have
180 = 40 + 40 + (2x + 30) = 80 + 2x + 30 = 110 + 2x
70 = 2x
x = 35
Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the following curve on the given interval y=2cos 3x on -- An integral that gives the arc length is a d x (Type exact answers.) Enter your answer in each of the answer boxes.
The arc length of [tex]y=2\cos(3x)[/tex] on the interval [tex][a,b][/tex] is
[tex]\displaystyle \int_a^b \sqrt{1 + (y')^2} \, dx = \int_a^b \sqrt{1 + (-6\sin(3x))^2} \,dx = \boxed{\int_a^b \sqrt{1+36\sin^2(3x)} \, dx}[/tex]
URGENT WILL GIVE BRAINLIEST
Answer:
626.7 [tex]cm^{2}[/tex]
Step-by-step explanation:
Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.
CIRCLE
A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7
RECTANGLE
A = l*w = 15*30 = 450
176.7 + 450 = 626.7 [tex]cm^{2}[/tex]
Answer: 626.7cm^2
Step-by-step explanation:
30 * 15 = 450
area of circle = πr^2
r = 15/2 = 7.5
[tex]7.5^2=56.25*pi=176.7[/tex]
450+176.7 = 626.7
The horizontal viewing angle is the angle subtended by a straight line from
each side of the screen to the seating position.
THX
THX Ltd., is a company founded in 1983 by George Lucas that develops
audio/visual reproduction standards for movie theaters. According to THX,
the viewing angle in a theater should be no less than 26 degrees and the best
viewing angle seems to be around 45-50 degrees and towards the center.
Suppose seat G11 has a horizontal viewing angle of 45°. This would be considered the best seat in the theater.
3. What is the measure of the arc the screen subtends?
The measure of the arc is given as π/2. See the explanation below.
What is an arc?An "arc" is a curve that connects two points in mathematics.
It can also be depicted as a section of a circle. It is essentially a portion of a circle's circumference. An arc is a kind of curve.
What is the calculation for the above solution?Note that the viewing angle is 45°.
Thus, the center angle is:
45 X 2 = 90°
Measure of the arc therefore is:
= (π/180°) x 90
= π/2
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which whole number is equal to the fraction 42/6
Answer:
7.
Step-by-step explanation:
Think of 42/6 as a division question.
42 ÷ 6.
The answer to this equation is 7.
A 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 3 feet from the wall
Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.
Pythagoras theorem, [tex]x^{2} + y^{2} = (12)^{2}[/tex] --->(1)
Given,[tex]\frac{dx}{dt}= 2feet/second[/tex] at x=3
Put x=3 in Pythagoras theorem equation (1)
[tex](3)^{2} + y^{2} = 144[/tex]
[tex]y^{2} = 144 - 9[/tex]
[tex]y^{2}[/tex] = 135
y = 11.61
Derive equation (1) w.r.t to 't'
[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex] ---->(2)
substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall
[tex]2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0[/tex]
12 + 23.22 [tex]\frac{dy}{dt}[/tex] = 0
[tex]\frac{dy}{dt}= \frac{-12}{23.22}[/tex]
[tex]\frac{dy}{dt} = -0.518[/tex]
Hence, using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
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11. What is the y-intercept of a line that passes through the point (5,17)
and has a slope of 4?
1. 17
2. 11
3. -3
4. 46
5. 2
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
y - intercept = -3[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Equation of straight line in point - slope form :
[tex]\qquad❖ \: \sf \:y - y1 = m(x - x1)[/tex]
( m = slope = 4, point (5 , 17) )
[tex] \qquad◈ \: \: \sf \: y - 17 = 4(x - 5)[/tex]
[tex] \qquad◈ \: \: \sf \: y - 17= 4x - 20[/tex]
[tex] \qquad◈ \: \: \sf \: y = 4x - 20 + 17[/tex]
[tex] \qquad◈ \: \: \sf \: y = 4x - 3[/tex]
Now, it's the form of line in slope - intercept form, ( slope = coefficient of x = 4 and y - intercept = -3 )
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex] \qquad◈ \: \: \sf \: y \: \: int = - 3[/tex]
What is the area of parallelogram ABCD?
A. 12 units²
B. 30 units²
C. 24 units²
D. 55 units²
Answer:
C, 24 units^2
Step-by-step explanation:
The formula for area of a parallelogram is base times height.
The height of the parallelogram is 4 units
The base of the parallelogram is 6 units
4 times 6 is 24
Hope this helps:)
Answer:
C. 24 units²
Step-by-step explanation:
To calculate the area of a parallelogram we use the following formula:
A = B*h (B: base, h: height)
The base of the parallelogram is 6 units and the height is 4 units
4*6 = 24 units but, the area is presented in square units so the answer is 24 units²
You are in a hot air balloon looking down at two ponds. Pond A which is in front of your balloon, is at an angle of depression that is your birth month (October), in degrees. (October = 10 degrees). Pond B, which is behind the balloon, is at angle of depression that is your Birth Day in degrees. (October 8 = 8 degrees). The balloon is 875 m in the air.
a. Draw and label a diagram
b. Find the distance from the hot air balloon to both Pond A and B
c. FInd the distance between the two ponds.
a. See attachment for the labelled diagram
b. Using the sine ratio, distance from the hot air to pond A is 5,038.9 m, while distance from the hot air to pond B is 6,287.1 m.
c. Distance between the two ponds is 1,263.5 m.
What is the Sine and Tangent Ratios?Sine ratio, is: sin ∅ = opposite side/hypotenuse length
Tangent ratio is: tan ∅ = opposite side/adjacent length.
a. The diagram with the appropriate labels is shown in the image attached below.
b. Use the sine ratio to find the distance from the hot air to pond A (CA) and to pond B (CB):
CA = hypotenuse
∅ = 10°
Opposite = 875 m
sin 10 = 875/CA
CA = 875/sin 10
CA ≈ 5,038.9 m (distance from the hot air to pond A)
CB = hypotenuse
∅ = 8°
Opposite = 875 m
sin 8 = 875/CB
CB = 875/sin 8
CB ≈ 6,287.1 m (distance from the hot air to pond B)
c. Distance between the two ponds, BA = BD + DA.
Apply the tangent ratio to find BD and DA
tan 8 = 875/BD
BD = 875/tan 8
BD = 6,225.9 m
tan 10 = 875/DA
DA = 875/tan 10
DA = 4,962.4 m
Distance between the two ponds = 6,225.9 - 4,962.4 = 1,263.5 m.
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There are 6 fifth grade classrooms that share 7 packs of paper. How much paper should each classroom get?
Answer:1.166 reams of paper.
Step-by-step explanation:
Just use simple division and divide 7/6.
Each classroom will get [tex]\dfrac{7}{6}[/tex] paper when there are 6 fifth grade classrooms that share 7 packs of paper.
A fraction is defined as a part of a whole. The upper part of the fraction is called the numerator, and the lower part is called the denominator.
Given that:
Number of fifth grade classrooms = 6
Number of packs of paper = 7
The number of paper each classroom get in fractions can be obtained by dividing the number of packs of paper by the number of fifth grade classrooms.
Each classroom get = [tex]\dfrac{Number \ of \ packs \ of \ paper}{ \ Number \ of \ fifth \ grade \ classrooms}[/tex]
Each classroom get = [tex]\dfrac{7}{6}[/tex]
Each classroom will get [tex]\dfrac{7}{6}[/tex] paper.
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Fill in the blank.
_______ are sample values that lie very far away from the majority of the other sample values.
Outliers are sample values that lie very far away from the majority of the other sample values.
We know that, an outlier is an observation that lies an abnormal distance from other values in a random sample from a population.
It differs significantly from other observations in a sample values.
Outlier is a value that is distant from the majority of the values in a data set.
For a scatter plot, an outlier is the point or points that are farthest from the regression line.
For example in the record of marks 25, 29, 7, 32, 85, 33, 27, 28 both 7 and 85 are outliers.
Therefore, outliers are sample values that lie very far away from the majority of the other sample values.
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The graph of the function f(x)=x2+12 is shown which stamen te describe the graph Check all that apply
A pattern has 77 yellow triangles to every 33 green triangles. What is the ratios of green triangles to yellow triangles?
Find the distance between the pair of points: (-3,-6) and (1,2).
d² = (y2 - y1)² + (x2 - x1)²
..............