If a circle has a radius that is 8 cm long, how long is the circle's diameter?
Answer: just add 8 + 8 and you will get 16
how many times greater is the value of the 2 in 204,936 than the value of the 2 in 124,936
When two fair dice are rolled, what is the probability that at least one of the numbers will be even??
A clown is juggling at a circus. The path of the ball is given by the parametric equations x=2cos t+2 and y=3sin t+3. In what direction is the ball moving?
-up and to the right
-counterclockwise
-down and to the right
-clockwise
1. B. Counterclockwise
2. C. (30,401)
3. A. t=2(x-3)
4. C. She should have taken both the positive and negative square root
5. C. y=x^2+8x-25/8
6. D. Hyperbola
7. A. Graph A
What are the foci of the ellipse given by the equation 100x2 + 64y2 = 6,400?
Quadratic relations and comic sections unit test part 1
11. a. (0, +/- 6)
The shortest side of a right triangle measures 88 m. the lengths of the other two sides are consecutive odd integersodd integers. find the lengths of the other two sides.
3. The roof of a castle tower is shaped like a cone. The base of the cone is 24 m across and the height is 16 m. The slant height of the roof, which is unknown, is the hypotenuse of the right triangle formed with the radius and the height of the cone. (a) Sketch the roof of the castle tower. Label the known lengths as described AND label the unknown length as x. (b) What is the slant height of the roof? SHOW YOUR WORK!
It takes 8 minutes for Byron to fill the kiddie pool in the backyard using only a handheld hose. When his younger sister is impatient, Byron also uses the lawn sprinkler to add water to the pool so it is filled more quickly. If the hose and sprinkler are used together, it takes 5 minutes to fill the pool. Which equation can be used to determine r, the rate in parts per minute, at which the lawn sprinkler would fill the pool if used alone?
A. 5/8 + 5r = 8
B. 5/8 + 5r = 1
C. 5(5/8) = r
D. 5/8 = 5r
Answer:
B,5/8+5r=8
Step-by-step explanation:
Which functions have real zeros at 1 and 4? Check all that apply.
f(x) = x2 + x + 4
f(x) = x2 – 5x + 4
f(x) = x2 + 3x – 4
f(x) = –2x2 + 10x – 8
f(x) = –4x2 – 16x – 1
Answer:
To find the zeros of a quadratic function, use the quadratic equation, [tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]. We find that the eqautions with zeros at 1 and 4 are b) x² -5x + 4 and d) -2x² + 10x - 8.
Step-by-step explanation:
a) x² + x + 4 --
[tex]x = \frac{-1 \pm \sqrt{1^2-4*1*4} }{2*1}\\x=\frac{-1 \pm \sqrt{1-16}}{2}[/tex]
Because the discriminant (the value inside the square root) is negative, this equation does not have real zeros, so it is not the answer.
b) x² - 5x + 4 --
[tex]x = \frac{5 \pm \sqrt{(-5)^2-4*1*4}}{2*1} \\x=\frac{5 \pm \sqrt{25-16}}{2} \\x = \frac{5 \pm 3}{2}[/tex]
Now, we calculate the two zeros by adding and subtracting the 3.
[tex]x = \frac{5+3}{2} \\x= \frac{8}{2} = 4\\\\x= \frac{5-3}{2} \\x= \frac{2}{2}=1[/tex]
The zeros of this function are 1 and 4, so it is included in our answer.
c) x² + 3x - 4 --
[tex]x = \frac{-3 \pm \sqrt{3^2-4*1*-4}}{2*1} \\x = \frac{-3 \pm \sqrt{9+16}}{2} \\x= \frac{-3 \pm 5}{2}\\\\x=\frac{-3+5}{2}=1\\x=\frac{-3-5}{2} = -4[/tex]
The zeros of this function are -4 and 1, so it is not the answer.
d) -2x² + 10x - 8 --
[tex]x = \frac{-10 \pm \sqrt{10^2-4*(-2)*(-8)} }{2*(-2)} \\x=\frac{-10 \pm \sqrt{100-64} }{-4} \\x = \frac{-10 \pm 6}{-4} \\\\x=\frac{-10 + 6}{-4} =1\\x = \frac{-10-6}{-4} =4[/tex]
The zeros of this function are 1 and 4, so it is included in our answer.
The probability that a dessert sold at a certain café contains strawberries is 26%. The probability that a dessert contains both strawberries and whipped topping is 18%. Find the probability that a randomly chosen strawberry dessert contains whipped topping. Round to the nearest tenth of a percent.
The probability that a strawberry dessert contains whipped topping is approximately 69.2%
We are given that the probability a dessert contains strawberries (P(S)) is 26%, or 0.26, and the probability that a dessert contains both strawberries and whipped topping (P(S and W)) is 18%, or 0.18.
To find the probability that a randomly chosen strawberry dessert contains whipped topping (P(W|S)), we use the conditional probability formula:
[tex]P(W|S) = \frac{P(S and W)}{P(S)}[/tex]
Substituting the given values, we get:
[tex]P(W|S) = \frac{0.18}{0.26} \approx 0.6923[/tex]
Rounding to the nearest tenth of a percent we get the probability that a randomly chosen strawberry dessert contains whipped topping to be 69.2%.
Which equation represents a parabola with a focus at (0,-2) and a directrix of y=6?
│FV│ = │VD│
Being D the directrix. Given that the focus F is on the y-axis and the directrix is parallel to the x-axis, then the vertex V will also be on this axis, so h = 0.
As │FV│ = │VD│, then:
[tex]k = \frac{6-2}{2}[/tex], that is the middle point of the segment FD, so:
V(0,2)
Now │FV│= │p│= │2-(-2)│=4
Given that the vertex and focus are below the directrix, then the parabola open down, therefore: [tex]p\ \textless \ 0[/tex]
Lastly, the equation is:
[tex]x^{2} = -4(4)(y-2) = -16y+32[/tex]
[tex]y = -\frac{ x^{2} }{16} + 2[/tex]
The equation of a parabola with a focus at (0,-2) and a directrix of y=6 is x^2 = -16(y - 2).
To find the equation of a parabola with a focus at (0,-2) and a directrix of y=6, you need to use the standard form of the equation of a parabola that opens upwards or downwards. The general form of this type of parabola is (x - h)^2 = 4p(y - k), where (h,k) is the vertex of the parabola, and p is the distance from the vertex to the focus (if the parabola opens upwards or downward) or to the directrix (if the parabola opens sideway).
Given that the focus is at (0,-2) and the directrix is at y=6, the vertex of the parabola will be located midway between them. The distance between the focus and directrix is 8 units, so the vertex will be 4 units from each, which puts the vertex at (0, 2). Therefore, h=0 and k=2.
Since the focus is below the directrix, our parabola opens downward, and the value of p is negative. The distance p is half the distance between the focus and directrix, so p=-4. Plugging these values into the general form, we get (x - 0)^2 = 4(-4)(y - 2), which simplifies to x^2 = -16(y - 2).
This is the equation that represents the desired parabola.
An antifreeze solution freezes at -100 °c. what is the freezing point on the fahrenheit scale? -82 °f -212 °f -88 °f -73 °f -148 °f
Your answer is the last option, -148°F
The formula to convert temperatures from Celcius to Farenheit is:
(C° x 9/5) + 32 or (C° x 1.8) + 32
So to solve, plug in -100°C and follow the order of operations (PEMDAS).
(-100 x 1.8) + 32
(-180) + 32
-148
-100°C is equal to -148°F
The freezing point of the antifreeze solution in Fahrenheit is -148 °F, calculated using the formula for converting Celsius to Fahrenheit.
To convert a temperature from the Celsius scale to the Fahrenheit scale, you can use the following formula: F = (C imes 9/5) + 32, where F represents the Fahrenheit temperature, and C represents the Celsius temperature.
In this case, we are given the freezing point of an antifreeze solution, which is -100 °C. Applying the formula, we get F = (-100 x 9/5) + 32. This calculation gives us F = (-180) + 32, which simplifies to F = -148 °F.
So, the freezing point of the antifreeze solution on the Fahrenheit scale is -148 °F.
using a fair coin and a fair six-sided number cube, what is the probability of tossing tails and rolling a multiple of 3?
[tex] |\Omega|=2\cdot6=12\\
|A|=1\cdot2=2\\\\
P(A)=\dfrac{2}{12}=\dfrac{1}{6}\approx17% [/tex]
On the Venn diagram, which region(s) represent the union of Set A and Set B (A⋃B)?
a. II
b. I and III
c. I, II, and III
d. I, II, III, and IV
Answer:
c. I, II, and III
Step-by-step explanation:
The union of two sets includes all elements from one set and all elements from the second set.
For our sets, this means all elements of set A, which includes region I and region II. It also means all elements of set B, which includes region III.
Thus the answer is regions I, II and III.
Answer:
C
Step-by-step explanation:
Just took the test
A supporting goods store sells 2 fishing reels and 5 fishing rods for $243. Later, they still 8 fishing reels and 6 fishing rods for $538. Find the price of each item.
Find the length of the curve yequalsthree fifths x superscript 5 divided by 3 baseline minus three fourths x superscript 1 divided by 3 baseline plus 8 for 1less than or equalsxless than or equals27.
The exact value of the arc length of the curve is 149.4 units
How to determine the exact arc length of the curve
From the question, we have the following parameters that can be used in our computation:
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
Also, we have the interval to be
-1 ≤ x ≤ 27
This means that the x valus are
x = -1 to x = 27
The arc length of the curve can be calculated using
[tex]\text{Length} = \int\limits^a_b {\sqrt{1 + ((dy)/(dx))^2}} \, dx[/tex]
Recall that
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
So, we have
[tex]\dfrac{dy}{dy} = x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}}[/tex]
This means that
[tex]\text{Length} = \int\limits^{27}_{-1} {\sqrt{1 + (x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}})^2}} \, dx[/tex]
Using a graphing tool, we have the integrand to be
[tex]\text{Length} = \dfrac{12x^\frac{5}{3}+15\sqrt[3]{x}}{20}|\limits^{27}_{-1}[/tex]
Expand and evaluate
[tex]\text{Length} = 149.4[/tex]
Hence, the exact arc length of the curve is 149.4 units
Help please !!!!!!!!!!!
Please help !!
20 points !!!!
Graph the function f(x)=−14x−2. Use the line tool and select two points to graph.
The graph of the function (f(x) = -14x - 2) is attached below and the two points from which line passes are (-0.143,0) and (0,-2).
Given :
Equation -- f(x) = -14x - 2
The following steps can be used in order to sketch the graph of the given function:
Step 1 - Write the given function.
f(x) = -14x - 2
Step 2 - Now, evaluate the x-intercept of the above function.
0 = -14x - 2
x = -1/7
Step 3 - Now, determine the y-intercept of the given function.
f(x) = -2
Step 4 - Now, graph the equation of a line that passes through the points (-1/7,0) and (0,-2).
The graph of the function is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
what does x2 + 11x + 24 look like on a graph
Name the property the equation illusrares 8+3.4=3.4+8
Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?
A) 17 miles
B) 32 miles
C) 37 miles
D) 40 miles
Answer:
D) 40 miles
Step-by-step explanation:
First we must find the distance between the mall and the house. The figure formed is a right triangle. The length of the side from the mall to the house forms the hypotenuse of the triangle. We can use the Pythagorean theorem to find the length:
a² + b² = c²
The two legs of the triangle, a and b, are 15 and 8:
15² + 8² = c²
225 + 64 = c²
289 = c²
Take the square root of each side:
√289 = √(c²)
17 = c
This makes the total distance
15+8+17= 40 miles
Hey! Pretty easy once you get the hang of these problems.
So you start off with the Pythagorean Theorem. Which is : a^2 + b^2 = c^2
Then just fill it in :
15^2 + 8^2 = c^2
225 + 64 = c2
289 = c^2
17 = c
And last :
15 + 8 + 17 = 40 MILES
hoped this helped!! :))
solve 3√5c*7√15c^2 please show your work
Which of the following are solutions to the equation below?
Check all that apply.
3x^2 + 27x + 60 = 0
A. 4
B. –4
C. –5
D. 5
E. –27
Answer:
The solutions are B. -4 and C. -5
Step-by-step explanation:
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
For [tex]\mathrm{}\quad a=3,\:b=27,\:c=60:\quad x_{1,\:2}=\frac{-27\pm \sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}[/tex]
[tex]x_1=\frac{-27+\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_1=\frac{-27+\sqrt{9}}{2\cdot \:3}\\\\x_1=\frac{-27+3}{2\cdot \:3}\\\\x_1=\frac{-24}{6} = -4[/tex]
[tex]x_2=\frac{-27-\sqrt{27^2-4\cdot \:3\cdot \:60}}{2\cdot \:3}\\\\x_2=\frac{-27-\sqrt{9}}{2\cdot \:3}\\\\x_2=\frac{-27-3}{2\cdot \:3}\\\\x_2=-\frac{30}{6} = -5[/tex]
A right triangle has sides if length 4,12 and 13 what is its perimeter
Answer:
29
Step-by-step explanation:
The perimeter is the sum of the side lengths:
4 + 12 + 13 = 29
The perimeter of the triangle is 29. (It is not a right triangle.)
___
A right triangle with side lengths 12 and 13 will have a short side of 5. Its perimeter is 30.
James pays $120.00 for golf clubs that are on sale fo 20% off at golf pros. At nine iron ,the same clubs cost $8.00'less than they cost at golf pros. They are on sale for 13% off
*Write An inequality then solve for the width.* The length of a rectangle is 12 more than its width. what values of the width will make the perimeter less than 96 feet? (Will give brainliest to best answer)
A class has 25 students - 15 girls and 4 boys. 5 girls and 4 boys are wearing blue. a student is picked at random. what is the probability that the studnet is either a boy or girl who is not wearing blue?
0.8 or 80%.
The question is asking for the probability that a randomly chosen student is either a boy or a girl not wearing blue. There are 25 students in total, with 15 girls and 10 boys. Out of these, 5 girls and 4 boys are wearing blue. Therefore, the number of girls not wearing blue is 15 - 5 = 10 girls. Since all boys are considered in the probability, regardless of what they wear, we have 10 boys. So, we have 10 girls not wearing blue and 10 boys, totalling 20 students that match the criteria out of 25.
The probability can be calculated as follows:
( P(\text{{boy or girl not wearing blue}}) = \frac{{\text{{number of boys and girls not wearing blue}}}}{{\text{{total number of students}}}} = frac{{20}}{{25}} = 0.8 ) or 80%.
Therefore, the probability that a student picked at random is either a boy or a girl who is not wearing blue is 0.8 or 80%.
In the diagram, the radius of the outer circle is 5cm and the area of the shaded region is 16π cm^2. What is the radius or the inner circle?
By using the area of the ring we will see that the radius of the inner circle is 3cm.
What is the radius of the inner circle?
I assume that we have some kind of ring. To get the area of the ring, we need to take the area of the circle defined by the outer radius of the ring, and subtract the area defined by the circle with the inner radius of the ring.
Remember that the area of a circle of radius R is:
A = pi*R^2
We know that:
The radius of the outer circle is 5cm, so its area is:
A = pi*(5cm)^2 = pi*25cm^2
And the area of the ring is pi*16 cm^2
Then the area of the inner circle should be such that:
pi*25cm^2 - A' = pi*16cm^2
Then, solving for A'
A' = pi*25cm^2 - pi*16cm^2 = pi*9cm^2 = pi*(3cm)^2
So the radius of the inner circle is 3cm.
If you want to learn more about circles, you can read:
https://brainly.com/question/1559324
Brainly a garden has width 13−−√ and length 713−−√. what is the perimeter of the garden in simplest radical form?
The correct answer is:
16√13.
Explanation:
The perimeter of a figure is found by adding together the lengths of all of the sides. The side lengths of this garden are: √13, √13, 7√13 and 7√13. This is because opposite sides in a rectangle are congruent.
Adding these together we have:
√13+√13+7√13+7√13 = (1+1+7+7)√13 = 16√13