Given the expression :
[tex]172+36.2+766.1+17.6[/tex]We will estimate the answer by rounding each number to the nearest 10
Look at the digit in the units place if 5 or greater add to the digit at the tens place
So,
[tex]\begin{gathered} 172\approx170 \\ 36.2\approx40 \\ 766.1\approx770 \\ 17.6\approx20 \end{gathered}[/tex]so, the answer will be :
[tex]170+40+770+20=1000[/tex]So, the answer is : 1,000
Help please I did them and got all wrong LOL..............
Answer:
1. Choice (2) 13
2. Choice (3) 8.1
3. Choice (3) 95 to 105 ft
4. Choice (3) 96 in
Step-by-step explanation:
All the problems use the Pythagorean theorem
The Pythagorean Theorem states that the sum of the squared sides of a right triangle equals the length of the hypotenuse squared.
[tex]c^{2} = a^{2} + b^{2}[/tex]
or
[tex]c = \sqrt{a^{2} + b^{2}}[/tex]
where c is the hypotenuse and a, b the shorter sides.
This means that given any two of the three sides of a right triangle we can compute the length of the third side
For example if we were given the hypotenuse c and side b, we can solve for side a by:
[tex]a = \sqrt{c^{2} - b^{2}}[/tex]
If we were given side a and asked to solve for side b then
b = \sqrt{c^{2} - a^{2}}
Frankly it does not matter which you choose as side a and side b.
Question 1
The distance from the foot of the ladder to the wall can be taken to be side a and is equal to 8ft
So b = 8ft
The length of the ladder is the hypotenuse c = 15 feet
[tex]a = \sqrt{c^{2} - b^{2}} \\\\a = \sqrt{15^{2} - 8^{2}}\\\\a = \sqrt{225 - 64}\\\\a = \sqrt{161}\\\\a = 12.68857754045 \\\\[/tex]
Rounded to nearest foot, that would be 13 feet So choice (2)
Question 2
The points J and K have the following coordinates as indicated on the graph.
J(-3, 2)
K (1, -5)
The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 2 dimensional plane, the distance between points (X1, Y1) and (X2, Y2) is given by the Pythagorean theorem:
[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
For:
(X1, Y1) = (-3, 2)
(X2, Y2) = (1, -5)
[tex]d = \sqrt {(1 - (-3))^2 + (-5 - 2)^2}\\\\d = \sqrt {(4)^2 + (-7)^2}\\\\d = \sqrt {{16} + {49}}\\\\d = \sqrt {65}\\\\d = 8.062258\\\\\text{Rounded to the nearest 10th it would be \boldsymbol{8.1}}\\\\[/tex] So choice (3)
Question 3
This again involves a right triangle as shown in the figure
The sides are a = AC = 60 and b = BC = 80 and we are asked to find the length of AC which is the hypotenuse of ΔABC
Use the Pythagorean Theorem directly
[tex]c = \sqrt{a^{2} + b^{2}}}\\\\a = \sqrt{60^{2} + 80^{2}}\\\\c = \sqrt{3600 + 6400}}\\\\c = \sqrt{10000}}\\\\c = 100}\\\\[/tex]
Answer 100 feet so choice (3): from 95 to 105 ft
Question 4
The brace is one of the shorter sides, with the platform top as the hypotenuse.
Let's use a for the brace, b for the 40 in side and c for the hypotenuse = 104 in
So we have to compute for b using the formula:
[tex]b = \sqrt{c^{2} - a^{2}}[/tex]
Using the given values, this would be:
[tex]b = \sqrt{104^{2} - 40^{2}}\\\\b = \sqrt{10816 - 1600}\\\\b = \sqrt{9216}\\\\b = 96\\\\[/tex]
which would be choice (3)
What is the solution to the following system of equations?x+y=5Ix-y=1
the initial equation is:
[tex]\begin{gathered} x+y=5 \\ x-y=1 \end{gathered}[/tex]So we can add bout of the equation so:
[tex](x+y)+(x-y)=5+1[/tex]and we simplify it so:
[tex]\begin{gathered} x+x+y-y=6 \\ 2x=6 \end{gathered}[/tex]now we solve for x so:
[tex]\begin{gathered} x=\frac{6}{2} \\ x=3 \end{gathered}[/tex]and with the value of x we can replace it in the first equation so:
[tex]3+y=5[/tex]and we solve for y:
[tex]\begin{gathered} y=5-3 \\ y=2 \end{gathered}[/tex]So the solution is x equal to 3 an y equal to 2
Find the standard form of the equation of the ellipse satisfying the given conditions.Endpoints of major axis: (4,12) and (4,0)Endpoints of minor axis: (8,6) and (0,6)
The Standard form of the ellipse is given as,
[tex]\frac{(x-a)^2}{a^2}+\text{ }\frac{(y-b)^2}{b^2}\text{ = 1}[/tex]The length of the major axis is given as,
[tex]\begin{gathered} 2a\text{ = 8} \\ a\text{ = }\frac{8}{2} \\ a\text{ = 4} \end{gathered}[/tex]The length of the minor axis is given as,
[tex]\begin{gathered} 2b\text{ = 12} \\ b\text{ = }\frac{12}{2} \\ b\text{ = 6} \end{gathered}[/tex]Therefore the required equation is calculated as,
[tex]\begin{gathered} \frac{(x-4)^2}{4^2}\text{ + }\frac{(y-6)^2}{6^2}\text{ = 1} \\ \frac{(x-4)^2}{16^{}}\text{ + }\frac{(y-6)^2}{36^{}}\text{ = 1} \end{gathered}[/tex]How many y-values are there for each x-value in the function represent by the graph
Answer: 1
Step-by-step explanation:
If the equation is a function there is one y-value for every x-value
Solve the inequality and graph the solution on the number line. 3 + 8x < 67
Answer:
The solution to the inequality is
x < 8
Explanation:
Given the inequality:
3 + 8x < 67
Subtract 3 from both sides of the inequality:
3 + 8x - 3 < 67 - 3
8x < 64
Divide both sides by 8
8x/8 < 64/8
x < 8
The solution to the inequality is
x < 8
The graph is shown below:
Solve each proportion.
4/5 = n/2
5/b = 9/5
The value of the first proportion is 1.6 and the value of the second proportion is 2.78.
What is a proportion?A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. A formula or claim shows that two ratios or fractions are equivalent.
According to the question,
The first proportion will be :
4/5 = n/2
n = 8/5
n = 1.6
The second proportion will be :
5/b = 9/5
b = 25/9
b = 2.78
Hence, the value of n will be 1.6 and the value of b will be 2.78 respectively.
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15 decreased by -7 is 22true or false why?explain
Given -
15 decreased by -7 is 22
To Find -
True or false
Step-by-Step Explaation -
15 decreased by -7 is 22
can be written as -
= 15 - (-7)
[as -(-a) = +a]
= 15 + 7
= 22
Final Answer -
Statement is True
A group of 15 people are ordering pizza.each person want 2 slices and each pizza has 15 slices.how many pizzas should they order
Learning Diagnostic Analytics Recommendations Skill plans Fifth grade > AA.12 Describe relationships among quadrilaterals SZT Complete the sentence below. A rhombus is a rectangle. always sometimes never Submit
A rectangle has 4 right angles.
A rhombus does not have 4 right angles,
So, A rhombus is sometimes a rectangle
I'm willing to give out 30 points so please this one is the most annoying one.
Match the example on the left with the corresponding property on the right.
3(x + 3) = 3x +9
2+3+4= 4+3 +2
4(2 x 3) = (4 x 2)3
6+ (7 + x) = (6 + 7) + x
those four up there you have to match with these three down here
Commutative Property
Associative Property
Distributive Property
Answer:
Commutative Property: 2 + 3 + 4 = 4 + 3 + 2
Associative Property: 4(2 x 3) = (4 x 2)3
Distributive Property: 3(x + 3) = 3x +9
Step-by-step explanation:
Hello, no worries!
These are just basic definitions that you need to remember, and then you'll be on track. The commutative property is when you change the order of the numbers you're either adding or multiplying.
For example, 2 + 3 = 3 + 2.
The associative property is when you simply have just three terms that when you switch the order in a way, the answer will be the same.
For example, 2(5 x 4) = 5(4 x 2).
Last, but not least, the distributive property is when you distribute a term in the parentheses and multiply them.
Hope this helped, and best of luck with the rest of your assignment. (:
The probability of a randomly selected adult in one country being infected with a certain virus is 0.005. In tests for the virus, blood samples from 19 people are combined. What is the probability that
the combined sample tests positive for the virus? ls it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least or person has the virus.
The probabilty that the combined sample wil test posiltive is 1.
(Round to three decimal places as needed.)
Answer: there is a 0.095% chance that one of the adults tests positive
Step-by-step explanation:
What is the answer to 2 tokens + 2 tokens
Answer: 4 tokens
Step-by-step explanation: 2+2=4
Answer:
4
Step-by-step explanation:
We can figure this out by counting. Using our fingers, we start with two, then when we add two more we have four fingers, or in this case tokens.
2. Which of the following represents a quadratic function? (Circle all that apply!) (2 pts)a, y = 9x2 + 4x - 6b. y = 3x + 8c. y = 1223 - 6x2 + 4x - 9
A quadratic function is a function in the form,
[tex]\begin{gathered} y=ax^2+bx+c \\ \text{where a, b, c are real } \\ a\ne0 \end{gathered}[/tex]Option A is a quadratic function,
Option B, is not a quadratic function because it is not the form of the equation written above and also,
[tex]a=0[/tex]Option C is also not a quadratic function because it has the highest degree of x to be 3.
In option D the function is given by the function is defined by
[tex]\begin{gathered} y=x^2 \\ \text{thus} \\ a=1\ne0 \end{gathered}[/tex]This implies that the function in option D is a quadratic function
Option E is not a quadratic function
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 6 ft high? (Round your answer to two decimal places.)
The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)
Define Volume of cone?
A pyramid having a circular cross section is called a cone. A right cone is a cone with the vertex located above the base's middle. Right circular cone is another name for it. If you know the height and radius of a cone and plug those values into a formula, you can quickly get the volume of a cone. Formula is , V = 1/3 πr²h
We have, dV/dt = 40 ft³/min
h = diameter where, h = 2r
so r = 1/2h
The formula for regular circular cone is,
V = 1/3 πr²h
put the value of r,
V = 1/ 3 * π * (1/2h)² * h
= 1/12 * π * h³
differentiate it, we get
dV/dt = 3/12 * π * h² * dh/dt
dh/dt = (dV/dt)/(3/12*π*h²)
we have, dV/dt = 40 ft³/min and h = 6
Put these values,
dh/dt = 40 / (3/12 * 22/7 * 6²) (∵ π = 22/7)
After solving, we get
dh/dt = 1.41 ft/min
Therefore, The height of the pile increasing when the pile is 6 ft high is 1.41ft/min (approx.)
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Which are the foci of the hyperbola represented by… Thanks!
The equation is given to be:
[tex]x^2-3y^2+12=0[/tex]We can write the equation in the standard form of the equation of a hyperbola to be:
[tex]\frac{\left(y-0\right)^2}{2^2}-\frac{\left(x-0\right)^2}{\left(2\sqrt{3}\right)^2}=1[/tex]Therefore, we have the following parameters:
[tex]\left(h,\:k\right)=\left(0,\:0\right),\:a=2,\:b=2\sqrt{3}[/tex]Recall the hyperbola foci definition:
[tex]\begin{gathered} \mathrm{For\:an\:up-down\:facing\:hyperbola,\:the\:Foci\:\left(focus\:points\right)\:are\:defined\:as}\:\left(h,\:k+c\right),\:\left(h,\:k-c\right),\: \\ \mathrm{where\:}c=\sqrt{a^2+b^2}\mathrm{\:is\:the\:distance\:from\:the\:center}\:\left(h,\:k\right)\:\mathrm{to\:a\:focus} \end{gathered}[/tex]Therefore, the value of c will be:
[tex]\begin{gathered} c=\sqrt{2^2+(2\sqrt{3})^2} \\ c=4 \end{gathered}[/tex]Therefore, the foci will be:
[tex]\begin{gathered} \left(h,\:k+c\right),\:\left(h,\:k-c\right)=\left(0,\:0+4\right),\:\left(0,\:0-4\right) \\ Foci=\left(0,\:4\right),\:\left(0,\:-4\right) \end{gathered}[/tex]The correct option is the FIRST OPTION.
Which degenerate conic is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone?
Circle
Parabola
One line
Two lines
One line is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone.
A rhombus's three-dimensional surface of rotation around one of its symmetry axes is known as a bicone or dicone in geometry. A bicone is a surface made by uniting two right circular cones that are congruent at their bases.
A 3D representation of a double cone {not shown indefinitely stretched). A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.
The part that intersects the plane is only the bus of the cone.
As a result, when a double cone's apex is cut by a plane parallel to the cone's slant edge, one line is created.
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Answer: one line
Step-by-step explanation:
use the zero product to find the solutions to the equation x^2 + 12 = 7x 1. x = -4 or x =3 2. x= -4 or x= -3 3. x= -3 or x =4 4. x=3 or x=4
Given the equation :
[tex]x^2+12=7x[/tex]Make all terms at one side:
[tex]x^2-7x+12=0[/tex]Factor the equation :
( x - 4 ) ( x - 3 ) = 0
Using the zero product to find x
So,
x - 4 = 0 OR x - 3 = 0
x = 4 OR x = 3
so, the answer is option 4. x = 3 or x = 4
Use the quadratic formula to solve for x.5x? - 7x=2Round your answer to the nearest hundredth.If there is more than one solution, separate them with commas.X == 0DO...Х5?
Given equation:
[tex]5x^2-7x\text{ = 2}[/tex]Re-arranging:
[tex]5x^2-7x\text{ -2 = 0}[/tex]Using quadratic formula:
[tex]x\text{ = }\frac{-b\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]a = 5, b = -7, c= -2
Substituting into the formula:
[tex]\begin{gathered} x\text{ = }\frac{-(-7)\pm\text{ }\sqrt[]{(-7)^2-4(5)(-2)}}{2\times5} \\ =\text{ }\frac{7\pm\sqrt[]{89}}{10} \end{gathered}[/tex]Writing as a decimal:
[tex]x\text{ = }-0.24\text{ or 1.64 (nearest hundredth)}[/tex]Answer:
x = -0.24, 1.64
1) Bob’s frog can travel 7 inches per jump, Kim’s frog can travel 9 inches, and Jack’s frog can travel 13 inches. If the 3 frogs start off at point 0 inches, how many inches will it be to the next point that all 3 frogs touch?
2) Two runners run around a circular track. The first runner completes a lap in 6 minutes. The second runner completes the track in 13 minutes. If they both start at the same place and the same time and go in the same direction, after how many minutes will they meet again at the starting place?
Answer:
See below
Step-by-step explanation:
LCM of 7 9 13
Prime factorization
9 = 3 x 3
7 = 7
13 = 13
LCM = 3 x 3 x 7 x 13 = 819 in
LCM of 6 and 13 is similarly 78 min
What is the area of the shaded region?____ square miles.
Finding the area of the shaded part means finding the area of the yellow triangle,
The exercise provide us the base and the height of the triangle, so we must replace these values in the next equation
[tex]A_{triangle}=\frac{b\cdot h}{2}[/tex]Where, b is the base and h is the height
[tex]A=\frac{5\text{ mi}\cdot4\text{ mi}}{2}=\frac{20\text{ mi}}{2}=10\text{ mi}[/tex]So, the area of the shaded region is 10 mi.
solve for the following system by using Elimination4x-2y=86x+6y=30
System
[tex]\begin{gathered} 4x-2y=8 \\ 6x+6y=30 \end{gathered}[/tex][tex]\begin{gathered} 3(4x-2y)=8 \\ 6x+6y=30 \\ \\ 12x-6y=24 \\ + \\ 6x+6y=30 \\ \\ 12x+6x-6y+6y=24+30 \\ 18x=54 \\ x=3 \end{gathered}[/tex]Now, for y
[tex]\begin{gathered} 4x-2y=8 \\ -2y=8-4x \\ 2y=4x-8 \\ y=\frac{4x-8}{2} \\ y=\frac{4\cdot3-8}{2} \\ y=\frac{12-8}{2} \\ y=\frac{4}{2} \\ y=2 \end{gathered}[/tex]Point O is on line segment NP . Given NO =5 and NP =20, determine the length OP .
If the point O is on the line segment NP, then:
[tex]NO+OP=NP[/tex]Replace for the given values and find the length of OP:
[tex]\begin{gathered} 5+OP=20 \\ OP=20-5 \\ OP=15 \end{gathered}[/tex]The length of OP is 15.
For a circle of radius 7 feet, find the arc length of a central angle of 6°.
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r = 7\\ \theta = 6 \end{cases}\implies s=\cfrac{(6)\pi (7)}{180}\implies s=\cfrac{7\pi }{30}\implies \underset{\textit{about 9 inches}}{s\approx \stackrel{ft}{0.73}}[/tex]
Look at this graph: 70 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 What is the slope?
EXPLANATION
As we can see in the graph, we need to take two ordered pairs in order to calculate the slope with the following equation:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Let's consider either one ordered pair, as (x1,y1)=(60,0) and (x2,y2)=(100,100), then the slope will be:
[tex]\text{Slope}=\frac{(100-0)}{(100-60)}=\frac{5}{2}[/tex]Answer: the slope is equal to 5/2.
Find the slope of the line that passes through (97, 21) and (54, -17).
Given data:
The first point given is (97, 21).
The second point given is (54, -17).
The slope of the line passing through the given points is,
m=(-17-21)/(54-97)
=-38/-43
=38/43
Thus, the slope of the line passing through the given points is 38/43.
Use the equation A=Pe^rt to answer each question. Show all work. First question
Answer:
$7209.78
Explanation:
To find the amount in the account after 6 years, we will use the following equation
[tex]A=Pe^{rt}[/tex]Where P is the initial amount, r is the interest rate and t is the time in years.
So, replacing P = $5000, r = 6.1% = 0.061, and t = 6 years, we get
[tex]\begin{gathered} A=5000e^{0.061t} \\ A=5000e^{0.061(6)} \\ A=5000e^{0.366} \\ A=5000(1.44) \\ A=7209.78 \end{gathered}[/tex]Therefore, the answer is $7209.78
Suppose that the age of all of a country's vice presidents when they took office was recorded. The collection of the ages of all the country's vice presidents when they took office is a A. PopulationB. ParameterC. Sample D. Statistic
Answer:
Population
Explanation:
A population is a complete group that has a common feature. A Sample is a part of that population and a statistic or parameter are measures of the sample or population.
In this case, we have the ages of all the country's vice presidents, so it is a population.
if n (A)=4, n (B) =9, and n(A ∩ B) =2; what is n( A U B)?
Given:
[tex]\begin{gathered} n(A)=4 \\ n(B)_{}=9 \\ n\mleft(A\cap B\mright)=2 \end{gathered}[/tex]To find:
[tex]n(A\cup B)[/tex]Using the formula,
[tex]\begin{gathered} n(A\cup B)=n(A)+n(B)-n(A\cap B) \\ =4+9-2_{} \\ =11 \end{gathered}[/tex]Hence the answer is 11.
true or false√3^(3√2) =(108)^1/6
False
Explanations:For the Left Hand side of the expression:
[tex]\sqrt[]{3}^{(3\sqrt[]{2})}[/tex]This can be simplified as:
[tex]\begin{gathered} 3^{\frac{1}{2}(3\sqrt[]{2})} \\ =3^{1.5\sqrt[]{2}} \\ =3^{2.12} \\ =\text{ }10.27 \end{gathered}[/tex]For the Right Hand Side of the expression:
[tex]\begin{gathered} (108)^{\frac{1}{6}} \\ =(108)^{0.167} \\ =\text{ }2.19 \end{gathered}[/tex]Since the Left Hand Side does not equal the Right Hand Side after simplification, the expression is not true
How do you write 6.01 × 10^2 in standard form?
