Using the line of best fit, it is found that the prediction of the forearm length of a man whose height is of 72 in is of 19.417 in.
What does the line of best fit state?It states that the predicted forearm length of a person of height x is given by:
y = -0.2967 + 0.2738x.
In this problem, the height is of x = 72 in, hence:
y = -0.2967 + 0.2738(72) = 19.417 in.
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Simmons earned a gross pay for the week of $694. If 8% was withheld for social security, 4% for Medicare taxes, 18% for income taxes, and $45 for insurance premiums, what was his net pay?
The net pay of Simmons will be $494 after the deductions.
What is net pay?The net pay is defined as the actual amount earned after the deductions of taxes and loan emi etc.
here simmon's total earning is $694
After the deductions the simmon will left with:
694x0.92x0.96x0.88=539.38
Now the insurance premiums are of $45
So the final amount will be
=539.38-45=494.38
Hence net pay of Simmons will be $494 after the deductions.
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The perimeter of a triangle is 84 meters. The longest side of the triangle is 7 meters less than twice the length of the shortest side ,x. The middle side is 7 meters longer than the shortest side. What is the length of each side of the triangle.
Hey ! there
Answer:
Smallest side = 21 mMiddle side = 28 mLongest side = 35 mStep-by-step explanation:
In this question we are given that perimeter of a triangle is 84 m , longest side of triangle is 7 meters less than twice the length of shortest side that is x and middle side is 7 meters longer than the shortest side .
And we're asked to find the length of each side of triangle.
So ,
Shortest side = x m Middle side = ( x + 7 ) m ( Because in question it is given that middle side is 7 metres longer than the shorter side )Longest side = ( 2x -7 ) m ( Because in question it is given that longest side is 7 m less than twice the length of shortest side )We know that ,
[tex]\underline{\boxed{\frak{Perimeter_{(Triangle)} = Sum \:of\: three\: sides}}}[/tex]
Solution : -
[tex] \longmapsto \qquad x +( x + 7) + (2x - 7) = 84[/tex]
Step 1 : Removing parenthesis and cancelling 7 with -7 :
[tex] \longmapsto \qquad x + x + \cancel{7} + 2x - \cancel{ 7 }= 84[/tex]
Step 2 : Adding like terms on left side :
[tex] \longmapsto \qquad 4x = 84[/tex]
Step 3 : Dividing with 4 on both sides :
[tex] \longmapsto \qquad \dfrac{ \cancel{4}x}{ \cancel{4}} = \cancel{\dfrac{ 84}{4} }[/tex]
On calculating further, We get :
[tex] \longmapsto \qquad \red{\underline{\boxed{\frak{ x = 21 \: m}}}}\quad \bigstar[/tex]
According to question ,
x = smallest sideHenceforth , smallest side of triangle is 21 meters .▬▬▬▬▬▬▬▬▬▬▬▬▬▬
x + 7 = middle side21 + 7 = 28Henceforth , middle side of triangle is 13 meters .▬▬▬▬▬▬▬▬▬▬▬▬▬▬
2x - 7 = longest side2(21) - 742 - 735Henceforth , longest side of triangle is 35 meters .Verifying : -
Now we are checking our answer by adding all the sides and equating it with given perimeter that is 84 metres .
21 + 28 + 35 = 8449 + 35 = 8484 = 84L.H.S = R.H.SHence , Verified .Therefore , our answer is correct.
#KeepLearningWhich picture shows a distance of 1/3 from Point A to Point B?
The correct answer is Choice A
F the positive z-axis points upward, an equation for a horizontal plane through the point (0,−2,−3) is
The equation for a horizontal plane through the point (0,−2,−3) is z= -3.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Let's assume n is the normal vector for the horizontal plane < 0, 0, 1 > .
The co-ordinate of the point is (0,−2,−3)
The general equation of a plane is -
[tex]n < x-x_0 , y - y_0, z-z_0 > =0\\\\ < 0,0,1 > \\\\0(x)+0(y+2) +1(z+3)\\\\z = -3[/tex]
Thus, The equation for a horizontal plane through the point (0,−2,−3) is z= -3.
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Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour. They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles. At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour. Mark plans to jog back the way they came. Jesse wants to find out who will arrive home first and by how much time. Which statements should he consider when solving the problem? Check all that apply.
A triangle. The sides are Capitol Street, H Street, and they hypotenuse is Florida Avenue.
Jesse will walk home a distance of approximately 2.0 miles as found by evaluating 1 squared + 1.75 squared = d squared and then 1 + 3.0625 = d squared.
Jesse will take about 0.4 hours to walk the rest of the way home as found by 2.0 = 5 (t).
Jesse will walk home a distance of approximately 2.25 miles as found by 1 squared + 1.75 squared = d squared and then 2 + 3.0625 = d squared.
Mark will jog home a distance of 2.75 miles.
It will take Mark about 0.23 hours to jog home as found by 2.75 = 12 (t).
Mark will jog home a distance of 2.25 miles.
Mark will get home about 0.17 hours (or 10 minutes) sooner.
Mark will get home about 0.21 hours (or 12.5 minutes) sooner.
Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of the other two legs of the right angle triangle.
Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour.
They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles. At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour.Here, Thus, Florida Avenue is hypotenuse triangular path and the other two sides are Capitol Street and H Street. The distance of Florida Avenue is,
[tex]1^2+1.75^2=d^2\\1+3.0625=d^2\\4.0625=d^2\\d=\sqrt{4.0625}\\d=2.0156[/tex]
Thus, Jesse walks 2.0156 with 5 miles per hour. Thus, the time taken by him is
[tex]t_J=\dfrac{2.0}{5}\\t_j=0.4\rm\;hr[/tex]
Mark plans to jog back the way they came which is 2.75 miles (1+1.75) long with speed of 12 miles per hour. Thus, the time taken by him is
[tex]t_M=\dfrac{2.75}{12}\\t_M=0.23\rm\;hr[/tex]
Thus, Jesse take 0.4 hours while Mark take 0.23 hours to reach back to home. The statements which should Jesse consider when solving this situation is statement 2.
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Which equals 4 quarts?
6 cups
16 pints
16 cups
O
12 pints
Answer:
16 cups
Step-by-step explanation:
1 quart = 4 cups
A box of of trading cards has 24-packs of cards in it. Only two of those packs contain limited edition cards.
A: What is the probability that a collector will find both limited edition cards if he buys only 2 packs?
B: What is the probability that he gets at least one limited edition card if he buys 3 packs?
The probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given that a box of trading cards contains 24-packs of cards in it. And Only two of those packs contain limited edition cards. Therefore, the probability of finding a limited edition card will be,
[tex]P = \dfrac2{24} = \dfrac{1}{12}[/tex]
The probability of not getting a limited edition card will be,
[tex]q = \dfrac{24-2}{24} = \dfrac{22}{24} = \dfrac{11}{12}[/tex]
Now, using the binomial distribution, the probability can be found.
A.) The probability that a collector will find both limited edition cards if he buys only 2 packs is
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=2) = ^2C_2 \cdot(\dfrac1{12})^2 \cdot (\dfrac{11}{12})^{(0)}\\\\P(x = 2) = 0.0069 \approx 0.007[/tex]
B.) The probability that he gets at least one limited edition card if he buys 3 packs can be written as,
The probability of at least a limited edition card
= 1 - Probability of not getting any limited edition card
The probability of getting no special edition card will be,
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=0) = ^3C_0 \cdot(\dfrac1{12})^0 \cdot (\dfrac{11}{12})^{(3)}\\\\P(x = 0) = 0.77[/tex]
Now,
The probability of at least a limited edition card
= 1 - Probability of not getting any limited edition card
The probability of at least a limited edition card = 1 - P(x=0) = 1-0.77 = 0.23
Hence, the probability that the collector gets at least one limited edition card if he buys 3 packs is 0.23.
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Enter an equation for the line of symmetry for the function f(x) = 2(x-5)^2 + 8.
so let's notice that, the equation is f(x) in x-terms, meaning the variable "x" is the independent and thus the parabola is a vertical parabola. Also let's notice that the equation is already in vertex form, keeping in mind that the axis of symmetry occurs for a vertical parabola at the x-coordinate.
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(x-\stackrel{h}{5})^2+\stackrel{k}{8}~\hfill \stackrel{vertex}{(5,8)}~\hfill \stackrel{\textit{equation for axis of symmetry}}{x=5}[/tex]
Help pls I don't understand
Not sure if I did this right Can someone help? Find the value of x.
Answer:
6
Step-by-step explanation:
Given :
⇒ The triangles are similar
⇒ The sides are in proportion
===============================================================
Solving :
⇒ [tex]\frac{6}{15+6} = \frac{8}{3x+10}[/tex]
⇒ [tex]\frac{6}{21}= \frac{8}{3x+10}[/tex]
⇒ [tex]\frac{2}{7} = \frac{8}{3x+10}[/tex]
⇒ [tex]\frac{1}{7}=\frac{4}{3x+10}[/tex]
⇒ 1(3x + 10) = 7(4)
⇒ 3x + 10 = 28
⇒ 3x = 18
⇒ x = 6
=============================================================
Solution :
The value of x is 6
How is the graph of the parent quadratic function transformed to produce the graph of y=-(2x+6)²+3?
O The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up
3 units.
O The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up
3 units.
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3
units.
The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3
units.
Answer:
the final option
Step-by-step explanation:
the negative sign causes a reflection, the +6 in the parentheses cases a 6 unit shift left and the +3 causes a 3 unit shift up
Work out length of AB
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
[tex] \large\underline{ \boxed{ \sf{✰\:Note }}}[/tex]
★ 1st let's know what is the given figure is and it's related concepts for solving !
➣ Given Triangle is a right angled triangle
➣ It is having 3sides let's know what are the name of these sides
➣ 1st AB is know as hypotenuse
➣ 2nd AC and is called Base of the triangle
➣ 3rd BC whích is know as perpendicular of the triangle
➣ Hypotenuse(H):-The side of a right triangle opposite the right angle.
➣ Perpendicular(P):- Exactly upright; extending in a straight line.
➣ Base(B):- it also known as the side opposite to hypotenuse
➣Perpendicular and base are know as the leg of right angled triangle
➣ We can easily find length of one missing side by using a theorem name as "Pythagorean theorem"
➣ Pythagorean theorem :- A mathematical theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of those of the two other sides
★ Note :- The Pythagorean theorem only applies to right triangles.
[tex] \rule{70mm}{2.9pt}[/tex]
★ Writing this theorem mathematically ★
[tex] { \boxed{✫\underline{ \boxed{ \sf{Pythagorean \: theorem \: ⇒ {Hypotenuse }^2={ Base }^2+ {Height }^2}}}✫}}[/tex]
★ Here ★
➣ Base (AC)= 22cm
➣ Perpendicular (height) (BC)= 8cm
[tex] \rule{70mm}{2.9pt}[/tex]
✝ Assumption ✝
➣ let Hypotenuse ( AB ) = "x"
[tex] \boxed{ \rm{ \pink ➛AB^2= AC^2+BC^2}}[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
✝ let's substitute values ✝
[tex]\rm{ \pink ➛x^2=22 ^2+8^2} \\ \rm{ \pink ➛x^2 = 484+ {64} } \\ \rm{ \pink ➛ {x}^{2} = 548 } \\ \rm{ \pink ➛= {x} = \sqrt{548} } \\ \rm{ \pink ➛ x = 2\sqrt{137} \: or23.4} \\ [/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
Hence Hypotenuse (AB) in the given triangle is of
[tex] { \boxed{✛\underline{ \boxed{ \sf{2\sqrt{137} \: or23.4\green✓}}}✛}}[/tex]
[tex] \rule{70mm}{2.9pt}[/tex]
Hope it helps !
SOMEBODY HELP! Math extra credi middle school
Step-by-step explanation:
5
A, d and e are the answer, multiplication/division never changes
6. yes, perpendicular lines are inside of each other always. how ever not all intersecting lines are perpendicular, for they're not 90° degrees.
3. ? (sorry)
4. ??
2. ?
The square root of 8+3 times the square root of 2 + the square root of 32
Answer:
[tex]9 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{8} + 3 \sqrt{2} + \sqrt{32} \\ \\ = \sqrt{ {2}^{2} \times 2} + 3 \sqrt{2} + \sqrt{ {2}^{4} \times 2 } \\ \\ = 2 \sqrt{2} + 3 \sqrt{2} + {2}^{2} \sqrt{2} \\ \\ = 2 \sqrt{2} + 3 \sqrt{2} + 4 \sqrt{2} \\ \\ = 9 \sqrt{2} [/tex]
Mariana buys a $10 pair of flip flops that is 15% off. How much change will Mariana receive when she buy=
them with a $20 bill.
Answer:
$11.50
Step-by-step explanation:
15% of 10 is 1.5
10-1.5=8.5
20-8.5=11.5
If 3n + 2 = 8, find the value of n.
Answer:
2
Step-by-step explanation:
3n+2=8
Collect like terms
3n=8-2
3n=6
Divide both sides by 3
3n÷3=6÷3
n=2
How can l use models to find part of a number?
Answer:
In math, number blocks are commonly used as models, where a small square equals 1, a long rectangle equals 10, and a large square equals 100. As models, blocks can be used for addition, subtraction, multiplication, and division. You can represent a problem given by using the correct models.
The volumes of two similar figures are given. The surface area of the smaller figure is given. find the surface area of the larger figure
V=2875 m^3
V = 1472 m^3
S.A. = 928 m^2
The surface area of the larger figure is [blank] m^2
Step-by-step explanation:
the surface area of a figure is always the result of a combination of multiplication(s) of 2 dimensions (side lengths).
and the volume of 3 dimensions (side lengths).
"similar figures" means that they share the same angles. and that there is one scaling factor that applies to all sides (and all other lines like heights).
so, no matter what sides are used to calculate the surface areas and the volumes, it is the same scaling factor used for each of them.
in a multiplication of 2 sides (for the area) the scaling factor is therefore applied twice and hence squared, in a multiplication of 3 sides it is applied 3 times and therefore cubed.
let's call the scaling factor f.
1472 × f³ = 2875
and then
928 × f² = large S.A.
let's use the first to get f :
1472 × f³ = 2875
f³ = 2875 / 1472 = (125 × 23) / (64 × 23) = 125/64
f = 5/4
f² = (5/4)² = 5²/4² = 25/16
large S.A. = 928 × 25/16 = 58 × 25 = 1450 m²
The perimeter, p, of a square is a function of its side length, s. The perimeter of the square is 28 inches or less. What is the domain of the function for this situation
The domain of the function for this situation is; s<= 7.
What is the domain of the function?It follows from the task content that the perimeter , p, of a square is a function of its side length, s. The perimeter of the square is 28 inches or less.
On this note it follows that;
P = 4s <= 28
Hence, it follows that; s<=7.
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Ximena gave out a survey to some students in her school about their favorite color. students could choose between red and blue. 180 of those surveyed said their favorite color was red. 55% of the students surveyed said their favorite color was blue. how many students were surveyed in total?
Answer:
Step-by-step explanation:
what we know is that 45% of the total was 180 (they voted red)
55% of the total voted blue.
To find the total, we need to set up a cross-multiplication equation
180/45 = ?/100
180 times 100 is 18000
18000/45 = 400
400 students were surveyed in total
we can check this by getting 55% of this, and adding it to 180.
If it equals to 400, then we're right.
55% of 400 = 220
220 + 180 = 400
please give brainliest! hope this helps :)
Lines m and n are parallel on a coordinate plane. Lines m and n are transformed by the same rotation, resulting in image lines s and t. Which statement describes the relationship between lines s and t?
The statement that best describes the relationship between lines s and t is: Lines s and t are parallel.
What are parallel lines?Parallel lines are as those lines that does not intersect one another despite being equal to each other.
Lines s and t are said to be parallel lines because they are cut by transversal which in turn means that transversal intersect lines s and t to make it parallel lines.
Therefore the statement that best describes the relationship is :Lines s and t are parallel.
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How many possible phone numbers can we make out of XXX – XXXX, where X can be any number 0-9? Show your work and leave your answer in either exponential or factorial form.
There are 10⁷ possible phone numbers from the digit 0 to 9.
What is Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set.
Here, there are total 10 possible digits (0 to 9) we can use to create 7 digit phone numbers.
For first place there are 10 possible digits.
similarly for second place again 10 possibilities and so on.
So total number of phone number = 10 X 10 X 10 X 10 X 10 X 10 X 10
= 10⁷
Thus, there are 10⁷ possible phone numbers from the digit 0 to 9.
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Possible phone numbers can be 10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!.
10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex]. (with repetition)
What is number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
There are 7 digit phone number represented with a XXX-XXXX .
So the first x can be 10 different numbers
let us take
10 ___ ___ ____ ____ ____ ____, but which ever number you use, it is then used up.
So then you only have 9 numbers left
10 x 9 x ___ x ___ x ___ x ___ x ___ .
Then, once that number is used it can't be used again, so on
10 x 9 x 8 x 7 x 6 x 5 x 4 (without repetition) = 10!/3!
If the repetition takes place then,
the first place have possibilities of 10 digits
10 __ __ - __ __ ___ __
Now, again repetition is allowed again there are possibilities of 10 digits.
10 10 __- __ __ __ __
and carrying the same way,
10 10 10 - 10 10 10 10= [tex]10^{7} =1,00,00,000[/tex].
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find the answer to this question: 205.04/4
pls help. due at 11:59
Answer:
see the attachment!
i hope this can help you.
Which represents the solution(s) of the graphed system of equations, y = x2 2x – 3 and y = x – 1? (1, 0) and (0, –1) (–2, –3) and (1, 0) (0, –3) and (1, 0) (–3, –2) and (0, 1)
Answer: the second choice: (0, - 2) and (1, 0).
Explanation:
1) The solution of a graphed system of equations is the points of intersection of the equations.
2) Hence, this method requires to graph each function in one Cartesian coordinate system.
3) To graph the function y = x² + x - 2, you can follow these steps
draw the perpendicular x(horizontal)-axis, and y(vertical)- axismark the divisions in each axis (1 unit is a good scale for this case)notice that y = x² + x - 2 is a parabolawrite y = x² + x - 2 in its vertex form following these steps:y = (x² + x) - 2
y + 1/4 = (x² + x + 1/4) - 2
y + 1/4 = (x + 1/2)² - 2
y = (x + 1/2)² - 2 - 1/4
y = (x + 1/2)² - 9/4
Compare with the vertex form y = (x + h)² + k, where the coordinates of the vertex are (h,k). Therefore, the vertex is (1/2, - 9/4).
The parabola open upwards (because the coefficient of the quadratic term is positive).Find the y-intercept (x =0) and x-intercepts (y = 0), and write a table with some values:x y = (x + 1/2)² - 9/4-2 0-1 - 2-1/2 -2.250 - 21/2 -1.251 02 44) To graph the function y = 2x - 2, you can follow these steps:
Use the same Cartesian coordinate systemNotice it is a lineThe slope is 2 (the coefficient of x)The y-intercept is - 2( the constant term)Build a table (use the same x-values used for the first graph)x y = 2x - 2-2 - 6-1 - 4-1/2 - 30 - 21/2 - 11 02 2The tables show that these points are common to the two functions: (0, - 2) and (1,0).
The graphs are shown in the figure attached.
You can see that the parabola (blue curve) and the line (purple line) intercept each other at those two points ( 0, - 2) and (1,0).
What is the center of a circle with equation (x-4)2 + y2 = 5?
Answer:
(4,0)
Step-by-step explanation:
standard equation for a circle is (x−h)^2 +(y−k)^2 =r^2
circle center: h, k with radius: r
(x-(+4)^2 + (y-0)^2 = 5
the center is (4, 0)
Let O be an angle in quadrant IV such that sec =
17/8
Find the exact values of cot and sin.
A town has a population of 2.33 x 104 and grows at a rate of 7% every year. Which a equation represents the town's population after 6 years?
Answer:
[tex]p = (2.33 \times {10}^{4})( {1.07}^{6} )[/tex]
A soup can has a diameter of 9.8 cm and a height of 13.2 cm. What is the approximate volume of 12 soup cans?
Answer:
about 11,948.05 cubic cm
Step-by-step explanation:
[tex]12 \times \pi( {4.9}^{2} )(13.2) = 11948.05[/tex]
Ingrid and Reed want to choose a tool that will allow them to measure the volume of a box. Which tool is most useful for Ingrid and Reed to measure the volume of a box?
