The volume of the rectangular prism which is as described in the task content is; 67½ cm³.
What is the value of the rectangular prism?It follows from the task content that the value of the rectangular prism which is as described is required to be determined.
Since the rectangular prism has width as six centimeters, the length as two and a half centimeters and the height as four and a half centimeters;
Volume = l × w × h
Volume = 2½ × 6 × 4½
Volume = 5/2 × 6 × 9 / 2
Volume = 67½ cm³.
Ultimately, the volume of the prism is; 67.5 cm³.
Read more on volume of prism;
https://brainly.com/question/12917973
#SPJ1
Express the area of the entire rectangle. Your answer should be a polynomial in standard form. An area model for a rectangle that has a height of x plus two and a width of x plus six. The rectangle is broken into four rectangles to isolate each term in the height and the width. The top left rectangle has a height of x and a width of x. The top right rectangle has a height of x and width of six. The bottom left rectangle has a height of two and a width of x. The bottom right rectangle has a height of two and a width of six.
The area of the entire rectangle as polynomial is x^2 + 8x + 12
Expressing the area of the entire rectangle as polynomialFrom the question, we have the following parameters that can be used in our computation:
Height = x + 2; Width = x + 6
Broken rectangles
Height = x; Width = xHeight = x; Width = 6Height = 2; Width = xHeight = 2; Width = 6The area of the rectangle is the product of the dimensions
Adding the heights and the width of the individual rectangles, we have
Height = x + 2; Width = x + 6
So, the area is
Area = (x + 2)(x + 6)
Expand
Area = x^2 + 8x + 12
Hence, the area expression is x^2 + 8x + 12
Read more about area at
https://brainly.com/question/24487155
#SPJ1
I need help on these
The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9
What are the radius and diameter properties of a circleA circle is a two-dimensional shape that is defined as a set of points that are equidistant from a single fixed point, called the center. The radius of a circle is the distance from the center to any point on the circumference. All radii of a circle are equal in length. While the diameter of a circle is a straight line passing through the center of the circle and touching two points on the circumference. The diameter is always twice the length of the radius.
For question (9):
the segments indicated as x and 6 are radii of the circle so;
x = 6
For question (10):
the radius = 31.6/2 = 15.8
also;
the radius = 6.9 + x
so;
x = 15.8 - 6.9
x = 8.9.
Therefore, the The length of the segment in circle (9) is the radius x = 6. And the length of the segment in (10) is x = 8.9
Read more about circle here:https://brainly.com/question/28162977
#SPJ1
Please help me with these 6th grade math questions.
Answer:
1. s < 40
2. w ≤ 12
3. D ≥ 110
4. D ≤ 3 1/2
5. w ≥ 30
6. m ≥ 45
7. t ≠ 21
8. c < 45
9. D > 1/5
10. s ≠ 45 5/6
11. h ≥ 48
12. P ≠ 5
An executive for a large company received gross pay of $200,000 for the year 2018. Determine the total amount of FICA tax that was paid on behalf of the employee. Round your answer to the nearest cent. Do NOT round until you calculate the final answer.
The total amount of FICA tax that was deducted from the executive's paychecks for the year 2018 is $10,860.80.
What is the total amount of FICA tax?The FICA tax is imposed on both employees and employers to fund Social Security and Medicare which are federal programs that provide benefits for retirees, the disabled and children of deceased workers.
The Social Security tax will be calculated on the maximum taxable earnings of $128,400:
= $128,400 x 6.2%
= $7,961.20
The Medicare tax will be calculated on the entire earnings:
= $200,000 x 1.45%
= $2,900.
The total FICA tax will be:
= Social Security tax + Medicare tax
= $7,960.80 + $2,900
= $10,860.80.
Read more about FICA tax
brainly.com/question/2288869
#SPJ1
The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). Which dolphin's weight differs most from the value predicted by this model?
The dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
Let's elaborate the model this way:
Snowflake's length - Pax's length = 8.2 - 7.6 = 0.6 ft
Snowflake's weight - Pax's weight = 549 - 519 = 30 lb
Ratio = 30/0.6 = 50 lb/ft
This means that for every foot of length, the dolphin has a variable weight of 50 lb.
However, if we multiply the ratio by the actual length of the two dolphins, we will have these results:
Snowflake = 50 × 8.2 = 410
Pax = 50× 7.6 = 380
Snowflake = Actual weight - Ratio× Length = 549 - 410 = 139
Pax = Actual weight - Ratio × Length = 519 - 380 = 139
The common difference is 139.
Therefore, the linear model that predicts the weight (y) of a dolphin given its length (X) is:
y = 139 + 50x
Now, let's use the linear equation or model to calculate the weight of the remaining four dolphins, as follows:
Blaze y = 139 + 50 × 6.8 = 479 ⇒ difference of 9 lb (488 - 479)
JoJo y = 139 + 50 × 5.8 = 429 ⇒ difference of 31 lb (460 - 429)
Corky y = 139 + 50 ×8.4 = 559 ⇒ difference of 2 lb (559 - 557)
Shadow y = 139 + 50 × 7.4 = 509 ⇒ difference of 8 lb (509 - 501)
Hence, the dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ1
The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to
create a linear model that predicts the weight (y) of a dolphin given its length (X). Which dolphin's weight differs most from th
value predicted by this model?
Name
Snowflake
Shadow
Corky
Pax
JoJo
Blaze
Length (ft)
8.2
74
8.4
7.6
5.8
6.8
Weight (lb)
549
501
557
519
460
488
Blaze
JOJO
Corky
Shadow
new car is purchased for 18700 dollars. The value of the car depreciates at
14.25% per year. To the nearest year, how long will it be until the value of the
car is 3000 dollars?
The minimum time required to depreciate the value of the car is 12 years.
Let us assumed the time to be t. Representing the formula for calculation of time-
Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]
Keeping the values in formula to find the time period
3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]
Solving the expression
[tex] {(0.8575)}^{t} [/tex] = 3000/18700
Cancelling zeroes common in numerator and denominator
3000/18700 = [tex] {(0.8575)}^{t} [/tex]
Taking log on both sides of the equation
t log 0.8575 = 30/187
Keep the value
t = log 0.8575 30/187
t = 12 years
Hence, it will take 12 years for value depreciation.
Learn more about depreciation-
https://brainly.com/question/1203926
#SPJ1
Helppp me please what is the formula for the carton 1/2*base of triangle*height of prism*height of prism ?
The volume of the triangular prism in the diagram is 10.5 in³
Calculating the volume of a triangular prismFrom the question, we are to calculate the volume of the the given prism.
The given prism is a triangular prism.
Volume of a triangular prism = Area of triangle × Height of prism
Thus,
Volume of the triangular prism = 1/2 × Base of triangle × Height of triangle × Height of prism
From the given diagram,
Base of triangle = 2 in
Height of triangle = 1.5 in
Height of prism = 7 in
Volume of the triangular prism = 1/2 × 2 in × 1.5 in × 7 in
Volume of the triangular prism = 10.5 in³
Hence,
Volume of the triangular prism is 10.5 in³
Learn more on Calculating the volume here: https://brainly.com/question/12591701
#SPJ1
Look at the figure shown. Which angle is obtuse?
Angle CDA.
Angle BAD.
Angle CBA.
Angle DAB.
A
60
B
120
120
C
60
D
The angle that is an obtuse angle (that is, greater than 90° but less than 180°) is 120°. The correct option is B. 120°
What is an obtuse angle?An obtuse angle is an angle that is greater than 90° but less than 180°. Thus, if x is an obtuse angle, the range of values for x are
90° < x < 180°
From the given question, we are to determine the angle which obtuse.
In the given figure, to determine the angle which is obtuse, we will determine the angle that is greater than 90° but less than 180°.
The angle that is greater than 90° but less than 180° is 120°.
Thus,
The obtuse angle is the angle that measures 120°
Learn more on Obtuse angle here: https://brainly.com/question/28175826
#SPJ1
If 5, x, y, and 40 are in geometric progression find x and y respectively
The values of x and y in the geometric progression are 10 and 20
Finding x and y in the geometric progressionFrom the question, we have the following parameters that can be used in our computation:
5, x, y, and 40
To calculate the values of x and y, we have
x/5 = 40/y
Cross multiply
So, we have
xy = 200
Set x = 10
So, we have
10y = 200
This gives
y = 20
So, we have
10/5 = 40/20 = 2 --- true
Hence, x is 10 and y is 20
Read more about sequence at
https://brainly.com/question/30499691
#SPJ1
Complete the ratio table.
Answer:
55
70
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
55 and 70
Step-by-step explanation:
5÷2=2.5
20÷8=2.5
45÷18=2.5
so
22×2.5=55
and
28×2.5=70
Explain how decimal place value is like place value with whole numbers. Use pictures or words to explain your thinking.
Write the equation for an exponential function, in the form ya x b. whose graph passes through the coordinate points (2, 12) and (3, 24).
The calculated equation for the exponential function is y = 3(2)ˣ
Calculating the equation for the exponential functionFrom the question, we have the following parameters that can be used in our computation:
Points = (2, 12) and (3, 24)
By definition, as exponential function is represented as
y = abˣ
Substitute the known values in the above equation, so, we have the following representation
ab² = 12
ab³ = 24
So, we have
b = 2
This means that
a(2)³ = 24
So, we have
a = 3
Recall that
y = abˣ
So, we have
y = 3(2)ˣ
Hence, the equation for the exponential function is y = 3(2)ˣ
Read more about exponential function at
https://brainly.com/question/2456547
#SPJ1
What is the square root of ab²?
O ab
Ob√a
Oa²b²
Ob²
Answer:
b[tex]\sqrt{a}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then
[tex]\sqrt{ab^2}[/tex]
= [tex]\sqrt{a}[/tex] × [tex]\sqrt{b^2}[/tex]
= [tex]\sqrt{a}[/tex] × b
= b[tex]\sqrt{a}[/tex]
Which linear equation is represented in the graph?
A. y = 2x – 1
B. y = –2x – 1
C. y = –2x + 1
D. y = 2x + 1
The equation of the line passing through the given points is y = -2x+1.
Given that is a line passing through two points (0, 1) and (2, -3) we need to find the equation of the line using them,
We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here (x₁, y₁) and (x₂, y₂) are (0, 1) and (2, -3),
Therefore, the required equation is =
y-1 = -3-1/2 (x-0)
y-1 = -2x
y = -2x+1
Hence, the equation of the line passing through the given points is y = -2x+1.
Learn more about equation of the line click;
brainly.com/question/21511618
#SPJ1
Use the distance and slope formula to prove that qaudlateal ABCD IS A PARLLAGRAM
Answer:79
Step-by-step explanation:
Ice Mountain Ski Resort is Philip's favorite place to go in the winter. This year, his aunt bought him a season pass. Philip used his season pass discount to get $13.75 off of the price of a new helmet. After the discount, the helmet's price was $116.25.
Answer:
$130
Step-by-step explanation:
price of helmet =discount+ price after discount
=$13.75+$116.25
=$130
The vertices of SRT are S (1, 4), R (2, 2) and T (1, 3). A reflection across the line _________ [ (A) x = 4, (B) x = 6, (C) y = –x + 5,(D) y = –x + 6] and then across the line _________ [ (A) y = 6, (B) y = 8, (C) y = –x + 10, (D) y = –x + 12] is the same as a translation of 4 units to the right and 4 units up because the lines are _________ [ (A) congruent, (B) parallel, (C) perpendicular, (D) similar].
The given reflection transformation is a rigid transformation, such that the dimensions are preserved
The statements that are true about the image of triangle ABC following a reflection Bout the the line y = 2·a are;
AB = RS
ΔABC ≅ ΔRST
m∠BAC ≅ m∠SRT
Reasons:
The given parameters are;
Triangle ΔABC is reflected across the line y = 2·x
Given that a reflection is a rigid transformation, we have;
The distance between two points on a preimage is the same as the distance between the corresponding points on the image;
Therefore;
ΔABC is congruent to ΔRST by Side-Side-Side SSS, rule of congruency, such that we have;
AB ≅ RS, BC ≅ ST, and AC ≅ RT
m∠BAC ≅ m∠SRT
m∠BCA ≅ m∠STR
m∠BAC ≅ m∠SRT
Therefore;
The true statements are;
AB = RS
ΔABC ≅ ΔRST
Therefore;
m∠BAC ≅ m∠SRT given that ΔABC ≅ ΔRST
Learn more here on reflection:
brainly.com/question/14136606
#SPJ1
complete question:
Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.
Question 3 options:
AB=RS
AB=2RS
ΔABC~ΔRST
△ABC≅ΔRST
m∠BAC=m∠SRT
m∠BAC=2m∠SRT
if A C B, then A n B = A U B
1) sometimes
2) never
3) always
if A C B, then A n B = A U B is always true
How to determine if A C B, then A n B = A U BThe statement "if A C B, then A n B = A U B" can be rephrased as "if A is a subset of B, then the intersection of A and B is equal to the union of A and B".
Every element of A is also an element of B. Therefore, the intersection of A and B contains all the elements of A.
On the other hand, the union of A and B contains all the elements of A and all the elements of B. Since A is a subset of B, all the elements of A are already included in B, so the union of A and B is just equal to B.
Therefore, we have:
A n B = A (since all the elements of A are in both A and B)
A U B = B (since A is a subset of B)
So A n B = A U B = B, which means that the original statement "if A C B, then A n B = A U B" is true
Learn more about set theory https://brainly.com/question/13458417
#SPJ1
Describe los Tipos de ángulos que se forman cuando divides un círculo en 4 partes iguales
The angles that you get when a circle is divided into 4 equal parts, would be four 90 degree angles.
How to describe the angles ?The reason these angles are called 'right angles' is because they create an exact 90-degree angle, signifying one fourth of a complete circle. Every specific angle is named as a 'quadrant,' as it covers a quarter or a quadrant of the circle.
These four perpendicular angles stand side by side - having in common not just one diameter of the circle but also a shared vertex, which is at the center of the circle. Together, they share uniformly the circle into four unique sections - each turning toward a distinct quadrant of the circle parallel to their placement.
Find out more on angles at https://brainly.com/question/31290586
#SPJ1
In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1,007 adults to learn about their major healthcare concerns. The survey results showed that 575 of the respondents lack confidence they will be able to afford health insurance in the future.
(a)
What is the point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future. (Round your answer to two decimal places.)
(b)
At 90% confidence, what is the margin of error? (Round your answer to four decimal places.)
(c)
Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future. (Round your answer to four decimal places.)
to
(d)
Develop a 95% confidence interval for this population proportion. (Round your answer to four decimal places.)
to
a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future is 0.57
b) At 90% confidence, the margin of error is 0.0324.
c) The 90% confidence interval is (0.5376, 0.6024).
d) The 95% confidence interval is (0.5314, 0.6086).
(a) The point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future can be found by dividing the number of respondents who lack confidence (575) by the total number of respondents (1,007):
Point estimate = 575/1007 = 0.57 (rounded to two decimal places)
(b) The margin of error can be calculated using the formula:
Margin of error = z√(p'(1-p')/n)
where z is the z-score associated with the desired level of confidence, p' is the point estimate, and n is the sample size. For a 90% confidence level, the z-score is 1.645.
Margin of error = 1.645√(0.57*(1-0.57)/1007) ≈ 0.0324 (rounded to four decimal places)
(c) The 90% confidence interval can be calculated using the formula:
Point estimate ± Margin of error
Substituting the values:
0.57 ± 0.0324
The 90% confidence interval is (0.5376, 0.6024) (rounded to four decimal places).
(d) The 95% confidence interval can be calculated in the same way, but with a different z-score. For a 95% confidence level, the z-score is 1.96.
Margin of error = 1.96√(0.57(1-0.57)/1007) ≈ 0.0386 (rounded to four decimal places)
0.57 ± 0.0386
The 95% confidence interval is (0.5314, 0.6086) (rounded to four decimal places).
To learn more about population click on,
https://brainly.com/question/14695181
#SPJ1
9. What is the measure of ZHLI?
H
K
30°
The missing angle of the given image is: ∠HLI = 150°
How to find the measure of the missing angle?There are different terms in this type of case when looking for missing angles and they include:
Corresponding angles
Supplementary angles
Opposite angles
Alternate angles
Now, we are given that:
∠JLI = 30°
We know that the sum of angles on a straight line is 180°. Thus:
∠HLI = 180° - 30°
∠HLI = 150°
Read more about missing angle at: https://brainly.com/question/28293784
#SPJ1
Let sin(2x) – sin(x) = 0, where 0 ≤ x < 2π. What are the possible solutions for x? Left-brace StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction Right-brace Left-brace StartFraction pi Over 3 EndFraction, StartFraction 5 pi Over 3 EndFraction right-brace Left-brace StartFraction pi over 6 EndFraction, StartFraction pi Over 2 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace
The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.
Given that:
sin(2x) – sin(x) = 0
Simplify the equation, then the value of 'x' is calculated as,
sin(2x) – sin(x) = 0
sin(2x) = sin(x)
2 sin x cos x = sin x
cos x = 1/2
cos x = cos (π/3, 5π/3)
x = π/3, 5π/3
The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ1
Abe purchased a candle at the candle store. The candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour. Write a function to determine the length of the candle, y, after burning for x number of hours.
The function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2
Given that, a candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour.
We need find function to determine the length of the candle, y, after burning for x number of hours.
Since, the melting rate of the candle is 1/2 per hour,
So, the function will be =
y = 9-x/2
Hence, the function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2
Learn more about functions, click;
https://brainly.com/question/21145944
#SPJ1
What is the base of the following natural logarithm?
In(x)
O 1
O 10
O e
The base of the natural logarithm ln(x) expression is 10
What is the base of the natural logarithm?From the question, we have the following parameters that can be used in our computation:
ln(x)
The base of the above expression is not stated
The general rule of logarithm is that when the base of the expression is not stated, then the base is 10
If the base of the expression is stated, then the expression would take the form
lnₐ(x), where the base is represented with the variable a
This means that the base of the natural logarithm ln(x) expression is 10
Read more about logarithm at
https://brainly.com/question/28041634
#SPJ1
What is the solution to the given linear-quadratic system: y = x + 5 and y = x² + 5?
Answer: 1 over 6
Step-by-step explanation:
The approximate areas of Nebraska and Massachusetts are listed below:
Nebraska: 2 x 105 square kilometers
Massachusetts: 2.73 x 104 square kilometers
What's the difference between the areas of the two states? Express your answer using
either standard notation or scientific notation.
The distance between the areas of the two states is A = 1.727 x 10⁵ km²
Given data ,
Let the area of Nebraska = 2 x 10⁵ km²
Let the area of Massachusetts = 2.73 x 10⁴ km²
The difference between the areas of Nebraska and Massachusetts A = the area of Nebraska - the area of Massachusetts
On simplifying the exponents , we get
A = 2 x 10⁵ km² - 2.73 x 10⁴ km²
Taking the common factor , we get
A = 10⁴ ( 20 - 2.73 )
A = 10⁴ ( 17.27 )
A = 1.727 x 10⁵ km²
Hence , the area is A = 1.727 x 10⁵ km²
To learn more about exponents click :
https://brainly.com/question/28966438
#SPJ1
What is the style of William Holman Hunt's The Awakening Conscience (1853)?
Pre Raphaelite
Impressionism
Nabis
Realism
Answer:
The style of William Holman Hunt's The Awakening Conscience (1853) is Pre-Raphaelite.
In the following diagram, ABCDABCD is a square. The coordinates of the vertices A,B,CA,B,C and DD are (3,3),(8,3),(8,8)(3,3),(8,3),(8,8) and (3,8)(3,8) respectively.
The square is dilated from the origin by a factor of 1111 to give A′B′C′D′A′B′C′D′.
What are the coordinates of point C′C′? (NEED THIS ASAP)
Answer:
Step-by-step explanation:
To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.
The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:
x-coordinate of C' = 1111 * 8 = 8888
y-coordinate of C' = 1111 * 8 = 8888
Therefore, the coordinates of point C' are (8888, 8888).
please show work asap thankyou so much
The net sales, =$20.98
The Goods available for sales= $2,045
The total cost of Goods sold=$1,955
Gross profit =$1,934.02
Net income = $1,395.98
How to determine the net sales from the last month's business income statement?The operating income (sales) = $7,240
The return on sales (ROS) = $345
The net sales (revenue generated) = ?
But ROS = operating income/net sales
Net sales = 7240/345;
= $20.98
The goods available for sale = beginning inventory+ new purchase = $725+$1320 = $2,045.
The total cost of Goods sold = Beginning inventory+goods available for sale - end inventory.
= 725+2,045- 815
= 2770-815
= $1,955
The gross profit = cost of goods sold (COGS) - total revenues.
= $1,955-$20.98
= $1,934.02
Net income = total operating expenses - gross profit
operating expenses = 1,750+1000+280+150+150 = $3,330
gross profit = $1,934.02
Net income = 3,330-1,934.02 = $1,395.98
Learn more about gross profit here:
https://brainly.com/question/30620212
#SPJ1
I need help on number 6