Answer:
C is 17.
Use Pythagorean theorem to find c (hypotenuse)
[We can use this theorem because it is a right triangle]
a^2 + b^2 = c^2
8^2 + 15^2 = c^2
c^2 = 289
c = sqrt(289) = 17
Answer: c = 17 cm
Step-by-step explanation:
Since this is a right triangle, we will use the Pythagorean theorem to solve. The a and b variables are legs, the c variable is the hypotenuse. Here, we are solving for the hypotenuse.
a² + b² = c²
8² + 15² = c²
64 + 225 = c²
64 + 225 = c²
289 = c²
c = [tex]\sqrt{289}[/tex]
c = 17
Side c has a length of 17 cm.
A disk is shaped like a flat circular plate. Its radius is 4.25 inches. To the nearest hundredth, what is the area of the disk? Use 3.14 for π.
Work Shown:
A = pi*r^2
A = 3.14*(4.25)^2
A = 56.71625
A = 56.72
3 yards 5 feet 6 inches
X 7=?
F- 32 yards 2 feet
6 inches
G-
33 yards 2 feet
6 inches
H- 33 yards 2 feet
9 inches
J- 34 yards 2 feet
6 inches
K- none of these
3 yards 5 feet 6 inches X 7 is 33.833333 yards. The correct option is K- none of these.
Numbers of yardsFirst step
One yard is 36 inches hence:
3 yards 6 inches=(36 inches×3)+6 inches
3 yards 6 inches=108 inches+6 inches
3 yards 6 inches=114 inches
Second step
5 Feet to inches=5 ft×12
5 feet to inches=60 inches
Third step
Yards=[(114 inches+60 inches)×7]/ 36 inches
Yards=(174 inches×7)/ 36 inches
Yards=1,218 /36 inches
Yards=33.833333
Therefore the correct option is K- none of these.
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She is serving hot coffee and cold coffee in two rectangular-shaped tanks, each with dimensions width 8.75 inches, length 8.75 inches, height 23 inches.
The hot coffee has a density of 5.8 oz/in3 and the cold coffee has a density of 3.5 oz/ in3
(A) What is the volume of the coffee in each tank?
Show all math work needed to complete this problem.
(B) What is the mass of the coffee in each the tank?
Show all math work needed to complete this problem.
(C) How many tanks can be placed on a table which can support a maximum weight of 800 lb?
Explain why or why not.
Show all math work needed to complete this problem.
Answer:
Part ADimensions of tank:
width = 8.75 inlength = 8.75 inheight = 23 in⇒ Volume of each tank = width × length × height
= 8.75 × 8.75 × 23
= 1760.9375 in³
Part BGiven:
Hot coffee density = 5.8 oz/in³Cold coffee density = 3.5 oz/in³mass = density × volume
⇒ mass of hot coffee = 5.8 oz/in³ × 1760.9375 in³
= 10213.44 oz (nearest hundredth)
⇒ mass of cold coffee = 3.5 oz/in³ × 1760.9375 in³
= 6163.28 oz (nearest hundredth)
Part CConvert the masses of the tanks from ounces to pounds
1 lb = 16 oz
⇒ mass of hot coffee tank = 10213.44 ÷ 16
= 638.34 lb (nearest hundredth)
⇒ mass of cold coffee tank = 6163.28 ÷ 16
= 385.21 lb (nearest hundredth)
If the table can hold a maximum of 800 lb:
hot coffee: 800 lb ÷ 638.34 lb = 1.25 (nearest hundredth)
cold coffee: 800 lb ÷ 385.21 lb = 2.08 (nearest hundredth)
Therefore, either:
1 tank of hot coffee OR2 tanks of cold coffeecan be placed on a table which can support a maximum weight of 800 lb
Felisha has 32 fluid ounces of pineapple juice. does she have enough pineapple juice to make one recipe?
Answer:
It depends
Step-by-step explanation:
Based on the given info it depends on how much the recipe calls for. 32 fluid ounces is equal to 4 cups, 1 quart, .25 gallons, 64 tablespoons, 192 teaspoons, and 2 pints. I really hope this answer helped you, and it honestly depends on how much the recipe calls for. :)
Answer:7
Step-by-step explanation:
Can anyone help solve this step by step?
Answer:
85.2 m²
Step-by-step explanation:
Perhaps one of the easiest ways to decompose this composite figure is to consider it as a rectangle with a triangle removed from it.
__
The vertical dimension of the missing triangle is 8-4 = 4 m. The horizontal dimension of the missing triangle is 11.4 -8.4 = 3 m. The overall rectangle, including the missing triangle, is 11.4 m wide and 8 m high.
The area of the figure is ...
area = rectangle area - triangle area
= (11.4 m)(8 m) -1/2(4 m)(3 m) = 91.2 m² -6 m² = 85.2 m²
The area of the shape is 85.2 square meters.
_____
Additional comment
The area of a rectangle is the product of its length and width:
A = LW
The area of a triangle is half the product of its base and height:
A = 1/2bh
In two or more complete sentences, determine the appropriate model for the given data and explain how you made your decision. (2,-1), (3,0.5), (6,1.5), (9,2)
Pease help :((
The solution to the question is arrived at using the knowledge of mathematical models.
What is a mathematical model?A mathematical model is a linguistic and mathematical concepts-based description of a system.
The appropriate model for the given data is:
Because there are discrepancies and no direct equation that can complete all of these points, a Least Square Regression Line is the best option for resolving this problem.
They could be outliers, so we need use a calculator to create a regression line to find the residual value.
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Part D
What is the probability of the next wolf caught in the park being unmarked? Write the probability as a fraction, a decimal number, and a percentage.
Animal Total in Park Number Marked
elk 5,625 225
wolf 928 232
cougar 865 173
bear 1,940 679
mountain goat 328 164
deer 350 105
moose 215 86
Answer:
636/928 = 137/200
0.685
68.5%
Step-by-step explanation:
What is the value of x?
Answer:
108
Step-by-step explanation:
x and 2/3 x are linear pair angles.
Sum of linear pair angles is 180.
x + 2/3 x = 180
3x/3 + 2x/3 = 180
( 3x + 2x )/3 = 180
5x/3 = 180
Cross multiply,
5x = 180 * 3
Divide 5 on both sides,
x = ( 180 * 3 )/5
= 36 * 3
x = 108
A video rental company offers a plan that includes a membership fee of $5 and charges $1 for every DVD borrowed. They also offer a second plan, that costs $47 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? What is that total cost of either plan?
Answer:
for $5 plan if he rents 47 dvd it will pay 47% as one DVS cost 1 $ .
Step-by-step explanation:
there were v crayons In a box.1/6 of the crayons were new.angie added another 24 new crayons to the box and there are 30 new crayons altogether.how many crayons were there in the box at first
Answer: 36
Step-by-step explanation:
If there are 30 new crayons, all you have to do is subtract the 24 new crayons Angie added, thus being six new crayons. Multiply this by 6 to get 36.
3) Jasmine says "I am 45 kilos". Yolander says, " I am 53 kilos". Both are measured to
the nearest kilogram.
What is the greatest possible difference between their masses? Show how you
worked out your answer.
spanish 45 kilis la respuesta seria que los yolander son 53kilos
please help me to answer
Answer:
7.92 cm²
Step-by-step explanation:
Area of Trapezium :
1/2 x (a + b) x h1/2 x (4.8 + 8.4) x 1.20.6 x 13.27.92 cm²A sample of 50 chewable vitamin tablets have a sample mean of 300 milligrams of vitamin c. nutritionists want to perform a hypothesis test to determine how strong the evidence is that the mean mass of vitamin c per tablet differs from 297 milligrams. state the appropriate null and alternate hypotheses.
The null hypothesis is that the mean mass of vitamin c per tablet does not differ from 297 milligrams
The alternative hypothesis is that the mean mass of vitamin c per tablet differs from 297 milligrams.
What is the null and alternative hypothesis?The null hypothesis usually states that there is no relationship between the population parameters. It is known as the true hypothesis. The alternative hypothesis states that there is a relationship between the population parameters.
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o Watch help video
A town has a population of 10000 and grows at 5% every year. What will be the
population after 5 years, to the nearest whole number?
Answer:
answers
Step-by-step explanation:
125000 Submit Answer.
Answer:
12763
Step-by-step explanation:
Based on the given conditions, formulate:
10000 x ( 5%+1)⁵
Evaluate the equation/expression: 12762.81563
Find the closest integer: 12763
Write a statement that indicates that the triangles in each pair are congruent.
Answer:
If the angle degree and size of triangle are similar or same, it is depicted as congruent.
Consider the sequence an = 9(0.4)n. which rule defines sn? sn = 6(0.4n) sn = 9(0.4n) sn = 6(1 – 0.4n) sn = 9(1 – 0.4n)
The rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
How to determine the expression for Sn?The formula of the sequence is given as:
an = 9(0.4)^n
The above means that:
The first term, a = 9Common ratio, r = 0.4The sum Sn is then represented as:
[tex]S_n =\frac{a(1 - r^n )}{1 - r}[/tex]
So, we have:
[tex]S_n =\frac{9 * (1 - r^n )}{1 - 0.4}[/tex]
Evaluate the difference and divide
[tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
Hence, the rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
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what does (5x3)+(4x2) equal
Answer:
23
Step-by-step explanation:
5 x 3 = 15
4 x 2 = 8
15 + 8
= 23
What are the solutions of the equation x^4+3x^2+2=0? Use u substitution to solve.
Answer:
Option BStep-by-step explanation:
Solve the equation in steps below
[tex]x^4+3x^2+2=0[/tex][tex]x^4+x^2+2x^2+2=0[/tex][tex]x^2(x^2+1)+2(x^2+1)=0[/tex][tex](x^2+2)(x^2+1) = 0[/tex][tex]x^2+2=0[/tex] or [tex]x^2+1=0[/tex][tex]x^2=-2[/tex] or [tex]x^2=-1[/tex][tex]x=\sqrt{-2}[/tex] or [tex]x=\sqrt{-1}[/tex][tex]x=\pm\ i\sqrt{2}[/tex] or [tex]x=\pm\ i[/tex]Correct choice is B
Someone please Help me please
In this question, we are presented with two triangles are required to find he missing sides in them. the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
Trigonometric RatioIn the first triangle, we need to use trigonometric ratio to find the missing side in the triangle
Data;
Angle = 45hypothenuse = [tex]8\sqrt{2}[/tex]adjacent = xTo find the adjacent side, we need to use cosine rule on this problem.
[tex]cos\theta = \frac{adjacent}{hypothenuse} \\cos45 = \frac{x}{8\sqrt{2} } \\x = 8[/tex]
The adjacent side is equal to 8 units
In the second triangle, we also need to use trigonometric ratio, but let's write down our data
angle = 30hypothenuse = 10opposite = ?adjacent = ?We can use both cosine and sine rule here or use one and use Pythagoras's theorem to find the other side.
[tex]cos \theta = \frac{adjacent}{hypothenuse} \\cos 30 = \frac{x}{10} \\x = 8.660[/tex]
The adjacent side is equal to 8.660, let's find the opposite side using sine rule
[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 30 = \frac{y}{10} \\y = 5[/tex]
And lastly, the value of the other angle is
[tex]90 + 30 + z = 180\\z = 180 - 120\\\\z = 60[/tex]
From the calculations above, the missing side in the first triangle is equal to 8 and the missing sides in the second triangle are 8.660, 5 and 60 for the adjacent, opposite and the second angle respectively
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Mary and her brother are saving their money to buy a laptop that costs $799. If Mary has $356.00 and her brother has $295.00, do they have enough money together to buy the laptop?
this is worth 40 points so pls help! I need this ASAP.
I also need COMPLETE solution
Answer:
Shown below.
Step-by-step explanation:
Test Marks Tally Frequency Percentage
1 8 8/60 = 0.133
2 6 6/60 = 0.100
3 5 5/60 = 0.083
4 5 5/60 = 0.083
5 5 5/60 = 0.083
6 8 8/60 = 0.133
7 6 6/60 = 0.100
8 7 7/60 = 0.116
9 4 4/60 = 0.066
10 5 5/60 = 0.083
Total 59 59/60 = 0.983
For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.
what is 90% of $90,000,000
Answer:
81000000
[tex]\frac{90}{100} *90000000\\ 90*900000\\ 9*9=81\\ then write all the zeros[/tex]
A triangle has a base of 8 cm and a height of 12 cm.
What is the area of the triangle?
Enter your answer in the box.
*box* cm2
Answer: 48 cm^2
Step-by-step explanation:
The equation for the area of a triangle is 1/2(base*height). Plug in the numbers to get an equation of 1/2(8*12). 8*12 = 96. Now divide by 2. 96/2 = 48.
Answer:
48 cm^2
Step-by-step explanation:
a triangle area is hb/2
so 8*12=96
96/2=48 therefore 48 is the answer.
The equation is the formula that relates the circumference of a circle to the radius. this gives us the ability to calculate pi if we physically measure a circle's circumference and radius. solve the equation for to get the formula you would use to perform this activity.
Answer:
π = C/(2r)
Step-by-step explanation:
The equation that relates the circumference of a circle to the radius is ...
C = 2πr
__
We can divide both sides of the equation by 2r to get an expression for π.
[tex]C=2\pi r\\\\\dfrac{C}{2r}=\dfrac{2\pi r}{2r}\\\\\boxed{\pi=\dfrac{C}{2r}}[/tex]
9. Find the slope of the line between the
coordinates (-6, -13) and (3, -1).
H.
F.
G.
314 43
J.
3/4 4/3
Answer:
The slope is 4/3
Step-by-step explanation:
The solution is in the image
Find the vertex and the axis of symmetry for the following functions.
a) y = 2x^3 + 4x
b ) y= -x^2+4x-5
Answer:
b
Step-by-step explanation:
its correct
Step-by-step explanation:
a)
y = 2x³ + 4x
a polynomial of 3rd degree cannot have an axis of symmetry.
it can only have a point of symmetry, like in this case.
(0, 0) is the point of symmetry, because due to the fact there is no squared term, any negative x values create exactly the same values (in absolute values) as their positive counterparts - just negative.
the vertex of a polynomial of 3rd degree is the point where the function changes directions.
that point for x³ is the origin, as it is for x. the factors only stretch the graph, but the vertex stays the same.
only if we had a term like (x+a)³ in the polynomial, this would shift the vertex.
so, the point of symmetry and the vertex are the same :
(0, 0).
b)
y = -x² + 4x - 5
the vertex form of a quadratic function is
f(x) = a(x − h)² + k
with (h, k) is the vertex.
x = h is the axis of symmetry.
we use "complete the square" to get it into that form.
-x² + 4x - 5 = -(x² - 4x + 5) = -(x - 2)² - 1
therefore,
y = -(x - 2)² - 1
h = 2, k = -1
the vertex is (2, -1)
the axis of symmetry is x = 2
what is 10x+15 if x is 10
The answer would be 115
Step-by-step explanation:
Find the area of the figure. (Sides meet at right angles.)
Answer:
44ft^2
Step-by-step explanation:
Break the shape into 3 rectangles, two 3 by 2's and one 4 by 8. (Get 4 by subtracting 3 from 7 for the left and right most side)
3 x 2 = 6 ft^2
since there's two rectangles you end up 6 + 6 so you get 12 ft^2
then 4 x 8 = 32 ft^2
add 32 and 12, get 44 ft^2
Frank joined a fitness club. He paid a $50 registration fee, and dues are $12 per month. Which expression can be used to find the average monthly cost of an x-month membership at the club?
Step-by-step explanation:
b is the answer y=50+12x/x
As we can get the information
the registration fee is fixed, but the dues is
increased with the Month.
so the average monthly cost
answer y=50+12x/x
Solve. 12 1/2 - (-4 1/2)
Answer:
17
Step-by-step explanation:
two negative signs makes a positive result