Only set (B) represents the side lengths of a right triangle.
In right triangle,
[tex](Hypotenuse)^{2} = (Perpendicular)^{2}+(Base)^{2}[/tex]
(A) [tex]8^{2} = 16[/tex]
[tex]12^{2} = 144[/tex]
[tex]15^{2} = 225[/tex]
225 ≠ 144 + 16
(B) [tex]10^{2} = 100[/tex]
[tex]24^{2} = 576[/tex]
[tex]26^{2} = 676[/tex]
676 = 576 + 100
(C) [tex]12^{2} = 144[/tex]
[tex]20^{2} = 400[/tex]
[tex]25^{2} = 625[/tex]
625 ≠ 400 + 144
(D) [tex]15^{2} = 225[/tex]
[tex]18^{2} = 324[/tex]
[tex]20^{2} = 400[/tex]
400 ≠ 324 + 225
Only (B) satisfies the condition.
Correct question,
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
(A) 8, 12, 15 (B) 10, 24, 26 (C) 12, 20, 25 (D) 15, 18, 20.
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Harry needs wood pieces to complete a project in woodshop class. He needs four pieces of wood that have a length of two and three fourths feet and five pieces of wood that are one and two thirds feet. What is the total amount of wood that Harry will need for the project?
The total amount of wood that Harry will need for the project is [tex]19\frac{1}{3}[/tex] feet.
What is a mixed fraction?
A mixed fraction is one that has both its quotient and remainder represented.
Or, a mixed fraction is a fraction that is created by combining a whole number and a fraction.
Given, 4 pieces of wood that have a length of [tex]2\frac{3}{4}[/tex] feet
And, 5 pieces of wood that have a length of [tex]1\frac{2}{3}[/tex] feet
So,
The total amount of wood = [tex]4*2\frac{3}{4} +5*1\frac{2}{3}[/tex]
= [tex]4*\frac{11}{4} + 5*\frac{5}{3}[/tex]
= [tex]11+ \frac{25}{3}[/tex]
= [tex]\frac{(11*3)+25}{3} = \frac{33+25}{3} = \frac{58}{3} = 19\frac{1}{3}[/tex]
Hence, the total amount of wood is [tex]19\frac{1}{3}[/tex] feet.
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PLEASE HELP ASAP
The result of 6 subtracted from a number n is at least 2. what numbers are solutions?
A.n-2>6;n>8
B.n-6>2;n>8
C.n+6>2;n<4
D.n+6>2;n>4
Answer:
B) n - 6 ≥ 2; n ≥ 8------------------------
Translate
6 subtracted from a number n ⇒ n - 6at least 2 ⇒ n - 6 ≥ 2Solution
n - 6 ≥ 2n ≥ 2 + 6n ≥ 8Option B is the closest one.
Answer:
b) n - 6 > 2 ; n > 8
Step-by-step explanation:
Given statement,
→ The result of 6 subtracted from a number n is at least 2.
Forming the inequation,
→ n - 6 > 2
Now the value of n will be,
→ n - 6 > 2
→ n > 2 + 6
→ [ n > 8 ]
Hence, the value of n is 8.
What is the solution of 2|7x – 4| + 3 = 51?
A urvey by the National Retail Federation found that women pend on average R146. On a Saturday
lunch. Aume the tandard deviation i R29. 44. Find the percentage of women who pend le than
R190. 00 on a Saturday lunch. Aume the variable i normally ditributed
0.68 is the variable is normally distributed when standard deviation is r29. 44.
What is standard deviation in math?
Your dataset's average level of variability is represented by the standard deviation.It reveals the average deviation of each statistic from the mean.A low standard deviation means that values are clustered close to the mean, whereas a high standard deviation means that values are typically far from the mean.μ = 146.21 σ = 23.44 x ~ n
P{ x < 160 } = ρ{ x - μ/σ < 160 - 146.21/29.44 }
= ρ{ z < 0.47 }
= 0.6808
≈ 0.68
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In ssa case for an obtuse angle, what is the maximum number of triangles that can be generate with the given information?.
Using the SSA method, the maximum number of triangles that can be generate is 1.
In the given question,
In SSA case for an obtuse angle, we have to find the maximum number of triangles that can be generate with the given information.
As we know that,
There cannot be a second obtuse angle if the specified first angle is already obtuse since the triangle's angle total would be greater than 180°. As a result, there is only one way to construct the triangle, making SSA a valid congruence theorem when the supplied angle is acute.
So the maximum number of triangles that can be generate is 1.
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A soda company would like to replace the label on a can of soda with a radius of 3 and one fourth cm. If the label touches end to end with no overlap, what is the length of the label? Use 22 over 7 for π.
143 over 56 cm
143 over 28 cm
143 over 14 cm
143 over 7 cm
The circumference of a circle is equal to the total length of its boundary. The length of label is 143 / 7 cm. the correct answer is option D.
What is a circle ?A circle is a geometrical shape having all of its points equidistant from a fixed point known as the center.
The angle subtended by a circle is 360°.
Given that,
the radius of the circle r = 3 + 1 / 4
= 13 / 4 cm
The length of label is equivalent to the circumference of circle having r = 13 / 4 cm.
The circumference is given as,
C = 2π × r
=> C = 2 × 22 / 7 × 13 / 4
=> C = ( 11 × 13 ) / 7
=> C = 143 / 7.
Hence, the length of the label is given as 143 / 7 cm.
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Answer:
d
Step-by-step explanation:
because i said so
How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?.
Degree of freedom for chi-square test for 10 categories will be 9.
What is chi- square test?
A test that evaluates how well a model matches real observed data is that the chi-square (χ²) statistic. A chi-square statistic can only be calculated with data that's random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a large enough sample.
The Formula for Chi-Square Is
χ(c)=²∑(Oₐ-Eₐ)₂/Eₐ²
where:
c=Degrees of freedom
O=Observed value(s)
E=Expected value(s)
Main Body:
Degree of freedom = total categories -1
so no. of categories= 10
Degree of freedom = 10 - 1
Hence degree of freedom = 9
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a line goes through the point (2,4) and has a slope of 3/2. Which of the following points is also on the line? Circle all that apply
The equation of the line passing through point (2,4) and having a slope of 3/2 is y = (3/2)x + 1.
What is the equation of line with the given point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Slope m = 3/2Point: (2,4)
x = 2y = 4Equation of line = ?First, we determine the y-intercept of the line 'b'.
Plug the slope and coordinates of the point into y = mx + b and solve for b.
y = mx + b
4 = (3/2)2 + b
4 = 3 + b
4 - 3 = b
b = 1
Now, plug the slope and y-intercept into y = mx + b to determine the equation of the line.
y = mx + b
y = (3/2)x + 1
Therefore, the equation of the line is y = (3/2)x + 1.
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In \triangle VWX,△VWX, \overline{WX}\cong \overline{VW}
WX
≅
VW
and \text{m}\angle V = 40^{\circ}.m∠V=40
∘
. Find \text{m}\angle X.m∠X.
The measure of m∠X is 70°
From the question, we have
Sum of interior angles of a triangle is equals to 180 degree
∠W+∠X+∠V=180°
2∠W+∠V=180°
2∠W+40°=180°
2∠W= 180°-40°
2∠W=140°
∠W = 70°
∠W = ∠X = 70°
Subtraction:
The process of removing items from a collection is represented by subtraction. Subtraction is represented by the minus sign. If, for instance, there are nine oranges stacked together (as shown in the above figure), and four of those oranges are then moved to a basket, the stack will contain nine minus four oranges, or five oranges. As a result, 9 minus 4 equals 5, or the difference between 9 and 4. Incorporating subtraction into other types of numbers is possible in addition to using it with natural numbers.
Complete question:
In triangle VWX above, overline VW = overline VX and angle V = 40 degrees. What is the measure of m∠X
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what's the numerical expression that has the same meaning as 5 multiplied by the sum of 67 and 86
The numerical expression will be;
⇒ 5 × (67 + 86) = 765
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division
Given that;
The algebraic expression is,
''5 multiplied by the sum of 67 and 86''
Now,
Write the mathematical expression as;
''5 multiplied by the sum of 67 and 86''
⇒ 5 × (67 + 86)
⇒ 5 × 153
⇒ 765
Thus, The numerical expression will be;
⇒ 5 × (67 + 86) = 765
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the primary tool for determining whether the assumptions made about the regression model are appropriate is
The primary tool for determining whether the assumptions made about the regression model are appropriate is residual analysis.
Regression analysis is a collection of statistical techniques used in statistical modelling to estimate the associations between a dependent variable and one or more independent variables. Regression analysis is a mathematical method for determining which of those factors has an effect.
Regression analysis is an effective statistical tool for examining the connection between two or more variables of interest. When the dependent and independent variables are connected in a linear or nonlinear form and the goal variable has a set of continuous values, it is extensively employed. As a result, regression analysis methodologies aid in the establishment of causal links between variables, as well as in the modelling of time series and forecasting.
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The midpoint of AB is M(-6, 1). If the coordinates of A are (-7,-3), what are
the coordinates of B?
Answer:
(-5,5)
Step-by-step explanation:
one day, river writes down the numbers river chooses one of the digits written down at random. what is the probability that river chooses a ?
The probability that river chooses a number "7" is 300/2889 or 100/963.
The numbers 1, 2, 3,..., 999 are noted.First, we count all the digits that have been recorded.
1 through 9 equals nine digits.
10 digits equals 2(99 - 10 + 1) = 2(90) digits.
100-999 = 3(999-100+1) = 3(900) digits.
Total digits: 9 + 2 (90) + 3 (900) = 2889
Digit 7 values between 1 and 999
7 appears 100 times every decade in the Units place (7, 017... 997)=10 X 10 times.
Seven appears ten times in the Tens position per century (70-79, 170-179,..., 970-979), which equates to 10 X 10 or 100 times.
The number 7 appears 100 times in the hundreds' place (700, 701,..., 799)
As a result, between 1 and 999, the number 7 will appear a total of 300 times.
Consequently, the likelihood of choosing "7" is equal to 300/2889.
= 100/963
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Jordan is a trucker. Today, he is hauling refrigerators that weigh 0. 16 tons each. His truck
weighs 15 tons when empty.
Write an equation that shows how the truck's weight in tons, y, depends on the number of
refrigerators in the truck, x.
The equation that show the relationship between the truck's weight in tons and the number of refrigerator in the truck x is y = 15 + 0.16x
The weight of the each refrigerator = 0.16 tons
The weight of truck when its empty = 15 tons
The weight of the truck = y
The number of refrigerators in the truck is x
Then the equation will be
y = 15 + 0.16x
Where y is the weight of the truck
x is the number of refrigerators
Hence, the equation that show the relationship between the truck's weight in tons and the number of refrigerator in the truck x is y = 15 + 0.16x
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What is 30% of 40?
Lou's class has 12 students in it. 8 of the students ran a race last weekend. What percent ran the race?
What is 30% of 40?
30% = 0.3
so:
0.3 * 40 = 12
_________________________
Lou's class has 12 students in it. 8 of the students ran a race last weekend. What percent ran the race?
8 out of 12 ran so:
8/12 = 2/3
2/3 = 0.6667
0.6667 as a percentage:
0.6667 * 100 = 66.667%
[if you need it rounded to two decimal places: 66.67%]
7 bags of red grape cost $24.50 4 bags of green grapes cost $15 what type of grapes is more expensive
Answer:
red grapes cost the most
Step-by-step explanation:
7 bags of red grape cost $24.50 4 bags of green grapes cost $15 what type of grapes is more expensive?
24.5/7 = $3.50 per bag
15/4 = $3.75 per bag
So, the red grapes cost more per bag.
Does anybody know the answer to this? (Math Extra Credit)
Answer: This looks like the periodic table, just find the variable and then you're good to go!
Step-by-step explanation:
Agustin bought c books. They were 6 dollars each. Write an equation to represent the total amount p that Agustin paid for the books.
The equation to represent the total amount paid for the book is p=6c.
What is equation ?An equation is a combination of two or more variables in which the two mathematics expressions are equal.
Given that,
Book bought by Agustin = c,
Price for the book = 6 $
The total amount paid by Agustin = Number of books × price of books
Amount =c×6,
p=6c $.
The amount paid by Agustin is p=6c $.
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PLEASE HELP NEED THIS TO BE DONE IN 10 MINUTES
The cost x of the Sennet family’s meal at a restaurant is $172.65, and they tip 20%. Write and use an equation to find the total cost y of the dinner.
Enter the correct answers in the boxes.
Answer: (x/5)+x=y
Step-by-step explanation:
The circumference of a circle is 14\piπ cm. Find its radius, in centimeters.
Answer:
Radius is 7π cm.
Step-by-step explanation:
Formula we use,
→ 2πr = 14π
→ 2r = 14π
Now the value of radius is,
→ 2r = 14 π
→ r = (14/2)π
→ [ r = 7π cm ]
Hence, the radius is 7π cm.
Answer:Answer:
Radius is 7π cm.
Step-by-step explanation:
Formula we use,
→ 2πr = 14π
→ 2r = 14π
Now the value of radius is,
→ 2r = 14 π
→ r = (14/2)π
→ [ r = 7π cm ]
Hence, the radius is 7π cm.
Step-by-step explanation:
Identify m∠LMN. The figure how triangle M L N. Angle L i a right angle. A meaure of angle M i given by the formula x plu 15 degree. Side L N lie on ray L O with endpoint L. Angle M N O i an exterior angle and it meaure i given by the formula 3 time x plu 15 degree
The angle of triangle ∠LMN = 60 degrees,
Right angle triangle MLN where at L it is a right angle ∠MLN=90 and the line LN of triangle MLN lies on the ray LO passes through LN it makes an exterior angle with MN it is given by 3x+15 degrees whereas angle M in the triangle MLN is given by ∠LMN = x+15 degrees.
By using the exterior angle relation that exterior angle =sum of two opposite internal angles,
Here, 3x+15=x+15+90,
We get x=45 degrees ,
So angle ∠LMN is x+15 which is 60,
Hence, The angle of triangle ∠LMN = 60 degrees.
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T Mobile charges $20 for the 1st phone plan and $6 per line added. Jenny has at most $60 she can spend for family. Write an inequality to show how many lines she can have.
Answer:
20 + 6L ≤ 60 :)
2. Find the turning point of y = x² + 4x - 3 by completing the square.
Answer:
turning point = (- 2, - 7 )
Step-by-step explanation:
the vertex form of a parabola is
y = a(x - h)² + k
where (h, k ) are the coordinates of the turning point ( vertex) and a is a multiplier.
given
y = x² + 4x - 3
to complete the square
add/ subtract ( half the coefficient of the x- term)² to x² + 4x
y = x² + 2(2)x + 4 - 4 - 3
y = (x + 2)² - 7 ← in vertex form
with turning point (- 2, - 7 )
a study of the fuel economy for various automobiles plotted the fuel consumption (in liters of gasoline used per 100 kilometers traveled) vs. speed (in kilometers per hour). a least squares line was fit to the data. here is the residual plot from this least squares fit. what does the pattern of the residuals tell you about the linear model? (a) the evidence is inconclusive. (b) the residual plot confirms the linearity of the fuel economy data. (c) the residual plot does not confirm the linearity of the data. (d) the residual plot clearly contradicts the linearity of the data. (e) none of the above
Based on the provided data and the residual plot from the least squares method fit, the pattern of the residuals tells you about the linear model that the residual plot clearly contradicts the linearity of the data. (Option D).
The least square method refers to the process of determining the best-fitting curve or line of best fit for the data points by decreasing the sum of the squares of the offsets (residual part) of the points from the curve. It is a mathematical regression analysis which is utilized to establish the best fit for processing data while providing a visual demonstration of the relation between the data points. The residual plot in the given situation indicated that the residual plot clearly contradicts the linearity of the data.
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Mickey simplified the expression below. He then checked his work by substituting 4 for x. He noticed his two values were not equal. What was Mickey’s error when simplifying?
Expression
Simplified Expression
2 x squared minus 4 x minus 9 minus x squared + 2 x + 3
x squared minus 6 x minus 6
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Mickey should have added 2 and 1 when combining the x squared terms.
Mickey should have added 9 and 3 when combining the constant terms.
Mickey should have added –4 and –1 when combining the x terms.
The correct option is, Mickey should have added –4 and 2 when combining the coefficients of the x terms.
Given,
The expression; 2x² - 4x - 9 - x² + 2x + 3
We have to simplify the expression;
To group and arrange an expression in such a way that it is easier to understand and solve is to simplify the expression.
We first group and find like terms and then add and cancel out
2x²-x²- 4x+2x - 9+ 3
=x²-2x-6
Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients
Therefore the correct option is
Mickey should have added –4 and 2 when combining the coefficients of the x terms.
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Lia’ pet hop ha 2 fih tank. Tank A contain maller fih who are fed 1 gram of food each per day. Tank B contain larger fih who are fed 2 gram of food each per day. If tank B contain 2/3 the number of fih that tank A contain, will Lia ever feed both tank the ame amount of food?
No, feeding both tanks the same amount of food is impossible.
Let's assume a pet store has two fish tanks and tank A contains Z number of smaller fish.
In tank A, she fed each fish one gram of food per day,
which equals Z*1, while
in tank B, she fed each fish two grams of food per day,
which is (2/3*Z)*2.
Let's now test the feasibility of feeding both tanks the same amount of food.
Z*1 = (2/3*Z) *2
Z = (2/3*Z) *2
3Z = 2*Z*2
3Z = 4 Z Lia will not be able to feed both tanks with the same amount of food because it is not possible.
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Alonso sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 349 visitors purchased no costume. 71 visitors purchased exactly one costume. 12 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.
The probability that the next person will purchase no costume as a percent is 80%.
Number of visitors who purchase no costume = 349
Number of visitors who purchase exactly one costume = 71
Number of visitors who purchase more than one costume = 12
Total number of visitors = 349 + 71 + 12 = 432
Probability of an event P(E) = Number of favorable outcomes (visitors who purchase no costume)/Total number of outcomes
⇒ P(E) = 349/432
⇒ P(E) = 349/432
Percent form of P(E) = (349×100)/432 = 80%
Hence the probability in percent form that next person will purchase no costume is 80%.
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A company designs a model pyramid with a square base that has side lengths equal to 5 inches and a height of 10 inches. To save costs in production, the lengths of the sides of the base are each reduced by one inch while the pyramid's height remains the same. What are the volumes of the original and the reduced size pyramids?
The volume of the original pyramid is, 250/3 cubic inches, and the volume of the reduced size pyramid is, 80/3 cubic inches.
What is the pyramid?
A pyramid is a structure that has triangular exterior surfaces that converge to a single step at the summit, giving it roughly a pyramidal shape in the geometric sense. Any polygonal form, including triangular and quadrilateral, can serve as the base of a pyramid. A pyramid has at least three outside triangle surfaces as a result.
Let, the pyramid has a square base of lengths 5 inches and the height is 10 inches.
Since,
Volume of pyramid = (l x b x h)/3
where,
l is the base length,
b is the base width and
h is the height.
Here, l = b = 5, h = 10
So,
V = (5 x 5 x 10)/3 = 250/3 cubic inches.
Now, to save costs in production, the lengths of the sides of the base are each reduced by one inch while the pyramid's height remains the same.
So, l = b = 4, h = 10
Therefore,
V = (l x b x h)/3 = (4 x 4 x 10)/ 3 = 80/3 cubic inches.
Hence, the volume of original pyramid is, 250/3 cubic inches and the volume of reduced pyramid is, 80/3 cubic inches.
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Juliet is standing atop a 15-‐foot balcony when she spots Romeo at an angle of depression of 5° . How far away is Romeo from the base of the balcony?
101.6 ft
190.5 ft
171.5 ft
87.6 ft
Romeo is 171.5 feet away from Juliet when she saw her at an angle of depression of 5 degrees.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
Given, Juliet is standing atop a 15-‐foot balcony when she spots Romeo at an angle of depression of 5°.
Here height is 15 feet and by interior alternate angles theorem angles is 5°
we have to determine the length of the adjacent side or base.
tan5° = 15/base.
base = 15/0.087.
base = 171.5 feet.
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Use identities to express the following in terms of sine and cose and then simplify your answer.
tan/sec
[tex]\cfrac{tan(\theta )}{sec(\theta )}\implies \cfrac{~~ \frac{sin(\theta ) }{cos(\theta ) } ~~}{\frac{1}{cos(\theta )}}\implies \cfrac{sin(\theta ) }{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\implies sin(\theta )[/tex]
