a) There are 6 sides, one of them having 6 on it. Therefore, the chances is 1/6.
b) Rolling a six or not rolling a six is guaranteed, because there is no other option. The probability is 1.
c) There are 6 sides, five of them not having a 6. So, the probability is 5/6.
A certain shade of blue is made by mixing 1.5 quarts of blue paint with 5 quarts of white paint. If you need a total of 16.25 gallons of this shade of blue paint, how much of each color should you mix
To create 16.25 gallons of a certain shade of blue paint, based on a ratio of 1.5 quarts of blue to 5 quarts of white, one would need to mix 15 quarts of blue paint with 50 quarts of white paint.
The student is asking how to scale a recipe for paint, which involves a ratio of blue paint to white paint, to create a specific amount of a new shade of blue. Given that the original ratio is 1.5 quarts of blue paint to 5 quarts of white paint, and the goal is to mix up 16.25 gallons of this shade, we need to calculate the amount of each color needed.
Step-by-Step Explanation:
First, identify the total number of quarts needed since the question includes quarts and gallons. Since there are 4 quarts in a gallon, multiply 16.25 gallons by 4 to convert to quarts.
16.25 gallons imes 4 = 65 quarts
Next, calculate the ratio of blue to total quarts, and white to total quarts. The original recipe has 1.5 quarts of blue paint out of a total of 6.5 quarts, as 1.5 quarts of blue plus 5 quarts of white equals 6.5 quarts.
Determine the proportions: Blue Paint = (1.5 / 6.5) times Total Quarts and White Paint = (5 / 6.5) times Total Quarts.
Calculate the required amounts: Blue Paint = (1.5 / 6.5) times 65 quarts = 15 quarts and White Paint = (5 / 6.5) times 65 quarts = 50 quarts.
In conclusion, to mix 16.25 gallons of the shade of blue paint, 15 quarts of blue paint and 50 quarts of white paint are required.
You would need 19.5 quarts of blue paint and 65 - 19.5 = 45.5 quarts of white paint to make a total of 16.25 gallons of the shade of blue paint.
To find out how much of each color should be mixed, we first need to convert the total amount needed into quarts.
16.25 gallons * 4 quarts/gallon = 65 quarts
Now, since the ratio of blue paint to white paint is 1.5:5, we can set up a proportion to find out how much of each color should be used:
1.5/5 = x/65
Cross multiplying:
5x = 1.5 * 65
5x = 97.5
x = 97.5 / 5
x = 19.5
So, you would need 19.5 quarts of blue paint and 65 - 19.5 = 45.5 quarts of white paint to make a total of 16.25 gallons of the shade of blue paint.
Find the polar equation of the conic with the focus at the pole, directrix y = -6, and eccentricity 4
Answer:
Choice B is correct
Step-by-step explanation:
The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.
Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;
[tex]r=\frac{k}{1-4sin(theta)}[/tex]
The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;
k= 4*6 = 24
The polar equation is thus given by alternative B
Answer:
B
Step-by-step explanation:
edge
Evaluate the log without a calculator ( Show your work )
The problem is in the image. I don't know how to write it.
Answer:
4
Step-by-step explanation:
Given in the question a logarithm expression
[tex]7^(log_{49}16 )[/tex]
We will use Exponent of Log Rule
[tex]b^(log_{b}k ) = k[/tex]
here b = 7
k = 16
So suppose
[tex]7^(log_{49}16 ) = x\\Take square on both sides\\(7^(log_{49}16 ) )^{2} = x^2\\49^(log_{49}16)= x^2[/tex]
Now, according to the rule
16 = x²
to find x only take square root on both sides of the equation
x = √16
x = 4
so [tex]7^(log_{49}16 )[/tex] = 4
The hour hand on a clock turns through an angle of 30° each hour.What is the measure of the total turn that the hour hand makes in 2 hours?
Answer:
60
Step-by-step explanation:
Since it turns 30 degrees each hour, it is simply 2 * 30 which is 60.
Two cards are drawn without replacement from standard deck of 52 cards. What is the probability that the first card is a spade and the second card is a heart and are these events independent?
103 / 204; Yes, they are independent events
1 / 17; No, they are dependent events
1 / 2; Yes, they are independent events
13 / 204; No, they are dependent events
Answer:
13 / 204; No, they are dependent events
Step-by-step explanation:
Total number of cards in the deck = 52
Total number of spades in the deck = 13
Total number of hearts in the deck = 13
Part 1: Calculating the Probability
Picking up the first card:
When picking the first card i.e spade, we have the option to pick 13 cards out of 52. So the probability will be 13/52
When first card is picked, the total number of cards will be reduced to 51 because we are not placing the card back in the deck
Picking up the second card:
When picking up the second card i.e. heart, we have the option to pick 13 cards out of 51. So the probability will be 13/51
The probability of picking a spade and then a heart is = 13/52 x 13/51 = 13/204
Part 2: Independent or Not
Note that, picking up a spade and not replacing it back is changing the probability of picking up a heart. In normal cases, picking up a heart from a deck will have the probability of 13/52, but since the we are not placing the card back the probability is changed to 13/51
Since, the probability of picking a heart is being changed by the previous event, we say that the two events are dependent.
Therefore, the correct answer will be final option: 13 / 204; No, they are dependent events
Use the given facts about the functions to find the indicated limit
Answer:
B. -12
Step-by-step explanation:
The given limit are;
[tex]\lim_{x \to -11} f(x)=-3[/tex] and [tex]\lim_{x \to -11} g(x)=4[/tex]
We want to find;
[tex]\lim_{x \to -11} (fg)(x)=\lim_{x \to -11} f(x)\times \lim_{x \to -11} g(x)[/tex]
We substitute the given limits to obtain;
[tex]\lim_{x \to -11} (fg)(x)=-3\times 4[/tex]
[tex]\lim_{x \to -11} (fg)(x)=-12[/tex]
Answer:
B
Step-by-step explanation: EDGE 2020
The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 7, find the absolute minimum value of f (x) over the interval [–3, 0].
0
2.5
4.5
11.5
[tex]f'(x)\ge0[/tex] for all [tex]x[/tex] in [-3, 0], so [tex]f(x)[/tex] is non-decreasing over this interval, and in particular we know right away that its minimum value must occur at [tex]x=-3[/tex].
From the plot, it's clear that on [-3, 0] we have [tex]f'(x)=-x[/tex]. So
[tex]f(x)=\displaystyle\int(-x)\,\mathrm dx=-\dfrac{x^2}2+C[/tex]
for some constant [tex]C[/tex]. Given that [tex]f(0)=7[/tex], we find that
[tex]7=-\dfrac{0^2}2+C\implies C=7[/tex]
so that on [-3, 0] we have
[tex]f(x)=-\dfrac{x^2}2+7[/tex]
and
[tex]f(-3)=\dfrac52=2.5[/tex]
Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). give a definition of what it means to be "95% confident" as an inference.
Answer:
In repeated sampling, 95% of the intervals constructed would contain the population mean.
Select the correct answer. What is the general form of the equation of a circle with center at (a, b) and radius of length m?
Answer:
see attachment.
Step-by-step explanation
see attachment
If the first step in the solution of the equation -x+6=5-3x is "subtract 5" then what would the next step be?
the next step would be add x to both sides to get x isolated
Answer:
i thought it was a but its b
Step-by-step explanation:
got it right on my test
Alan takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Alan is taking a combined total of 19 credit hours at the two schools.
Suppose that he is taking w credit hours at Westside. Write an expression for the combined total dollar amount he paid for his class fees.
Total he payed (in dolllars) = ?
Answer:
Step-by-step explanation: If w is hours at Westside, then (18-w) is the number of hours taken at Pinewood.
Cost to westside = 98w. Cost to Pinewood = 115(18-w).
Total cost = 98w + 115(18 - w) = 2070 - 17w.
[I guess there should be some constraints like 0 > w > 18]
I put it as "greater than" rather than "greater than or equal" because the problem states he takes classes at both schools, hence he has to take at least something at Westside, and similarly he has to take something at Pinewood so he would not take all 18 hours at Westside.
Answer:
98 × w + $115(19-w)
Step-by-step explanation:
We are given that Alan takes classes at both Westside Community College, where class fees are $98 per credit hour, and Pinewood Community College, where class fees are $115 per credit hour.
If Alan is taking a total of 19 credit hours at the two mentioned schools, we are to write an expression for the combined total dollar amount he paid for his class fees.
Considering the fees per credit hour mentioned for each school, we can write the total payed fees as:
[tex]98 \times w + $115(19-w)[/tex]
the d string on a violin has a frequency of 293 hz when it is in tune. calculate the period.
Answer:The Time (period) is 0.003 s
Step-by-step explanation:
The period is equal to Time.
the formula for calculating Time (period) is:
Time (period)= 1/frequency
frequency= 293 hz
Time (period) = 1/293
= 0.003 s
Answer:
Period = 0.0034 seconds
Step-by-step explanation:
It is given that,
The d string on a violin has a frequency of 293 Hz when it is in tune. We have to find its period. The relationship between the time period and the frequency is given by :
[tex]T=\dfrac{1}{\nu}[/tex]
Here, [tex]\nu=293\ Hz[/tex]
So,
[tex]T=\dfrac{1}{293\ Hz}[/tex]
T = 0.0034 seconds
Hence, the period of the d string on a violin is 0.0034 seconds.
A jar contains 30 marbles. It has 10 red, 6 black and 14 green marbles. Two marbles are drawn, the first is not returned before the second one is drawn. What is the probability that both marbles are green?
P(Both Green) =
14 / 169
P(Both Green) =
91 / 435
P(Both Green) =
7 / 15
P(Both Green) =
49 / 225
Answer:
The correct answer option is P (both green) = 91 / 435
Step-by-step explanation:
We are given that in a jar containing 30 marbles, 10 are red, 6 are black and 14 are green.
Two marbles are drawn and the second one is drawn without returning the first marble and we are to find the probability of getting green marbles both time.
P (both green) = [tex] \frac { 1 4 } { 3 0 } \times \frac { 1 3 } { 2 9 } [/tex] = 91 / 435
How to put Twelve birds are 3 more than twice the number of birds Rhonda saw yesterday as an equation
First set up birds is +3 than 2x the number of birds Rhonda saw
Rhonda's birds = r
Current set of birds = c
c = 2r + 3
Current birds are equal to three more than double the amount of birds rhonda saw
What is the equation of the line, in slope-intercept form, that passes through the point (6,−1) and is perpendicular to the line y=2x−7?
A)y=2x+13
B)y=−12x+2
C)y=12x−4
D)y=12x+132
did you mean to put. y= -1/2x+2 for choice b? because that's what I got as a solution
How much simple interest would x dollars earn in 13 months at a rate of r percent
Answer:
[tex]I=\frac{13xr}{1,200}[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Simple interest Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal form
t is Number of Time Periods in years
in this problem we have
[tex]t=(13/12)\ years\\ P=\$x\\r=(r/100)[/tex]
substitute in the formula above
[tex]I=x(r/100)(13/12)[/tex]
[tex]I=\frac{13xr}{1,200}[/tex]
Final answer:
To calculate simple interest for x dollars at an rate of r percent over 13 months, convert r percent to a decimal and time to years, then use the formula I = x × (r/100) × (13/12). For example, $100 at 5% interest for 13 months would earn approximately $5.42 in simple interest.
Explanation:
The calculation of simple interest for a principal of x dollars at a rate of r percent over 13 months involves a few straight-forward steps. The formula for the simple interest is given by:
I = P × r × t
Where I represents interest, P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time the money is invested or borrowed for, in years.
To convert the rate r percent to a decimal, divide by 100. Then, convert the time of 13 months to years by dividing by 12.
Thus, the simple interest formula for this question becomes:
I = x × (r/100) × (13/12)
For example, if you deposit $100 into a savings account with a simple interest rate of 5% for 13 months, the interest earned would be calculated as follows:
I = 100 × (5/100) × (13/12)
This results in:
I = 100 × 0.05 × 1.08333
I = $5.42 (approximately)
The simple interest earned, in this case, would be approximately $5.42.
Consider that the length of rectangle A is 10 cm and its width is 6 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 6 cm. B) A rectangle with a length of 15 cm and a width of 9 cm. C) A rectangle with a length of 14 cm and a width of 7 cm. D) A rectangle with a length of 12 cm and a width of 8 cm.
Answer:
B) A rectangle with a length of 15 cm and a width of 9 cm
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
Verify each cases
case A) A rectangle with a length of 9 cm and a width of 6 cm
[tex]\frac{10}{9}\neq \frac{6}{6}[/tex]
therefore
The rectangle case A) is not similar to rectangle A
case B) A rectangle with a length of 15 cm and a width of 9 cm
[tex]\frac{10}{15}=\frac{6}{9}[/tex]
[tex]\frac{2}{3}=\frac{2}{3}[/tex]
therefore
The rectangle case B) is similar to rectangle A
case C) A rectangle with a length of 14 cm and a width of 7 cm
[tex]\frac{10}{14}\neq \frac{6}{7}[/tex]
therefore
The rectangle case C) is not similar to rectangle A
case D) A rectangle with a length of 12 cm and a width of 8 cm
[tex]\frac{10}{12}\neq \frac{6}{8}[/tex]
therefore
The rectangle case D) is not similar to rectangle A
Answer:
A rectangle with a length of 15 cm and a width of 9 cm.
Step-by-step explanation:
In similar rectangles, the ratios of the corresponding sides are equal.In similar rectangles, the ratios of the corresponding sides are equal.
[tex]\frac{length}{width}[/tex] → [tex]\frac{10}{6}[/tex] = [tex]\frac{5}{3}[/tex] and [tex]\frac{15}{9}[/tex] = [tex]\frac{5}{3}[/tex]
-2(-25)+2y=44 solve for y please!!! semi-urgent! I will give the correct answer brainliest!!!
Answer:
y = -3
Step-by-step explanation:
First, subtract 44 from both sides of the equation to set it equal to 0. This will give you 6 + 2y = 0. Then, subtract 6 from both sides, leaving you with 2y = -6. Then just divide both sides by 2 to isolate the y and give you your answer. -6 divided by 2 is -3. y = -3
Triangle ABC is similar to triangle PQR, as shown below: Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB = c, BC = a, and AC = b. Triangle PQR has sides PQ = r, QR = p, and PR = q. Angle CAB is congruent to angle RPQ. Angle ABC is congruent to angle RQP. Angle ACB is congruent to angle QRP. Which ratio is equal to r:c? c:p p:a r:a q:c
Answer:
p:a
Step-by-step explanation:
given: AB=c, BC=a, CA=b
PQ=r, QP=p, PR=q
also , ∠CAB ≅ ∠RPQ,--------- (1)
, ∠ABC ≅ ∠RQP,---------(2)
and, ∠ACB ≅ ∠QRP,---------(3)
FROM (1), (2) AND (3),
we can say that a=p, b=q, c=r
therefore, the triangles are congruent (S.S.S congruence criteria),
also then, r:c=1
then the ratio equal to r:c, will be p:a ( since p=a and p:a would be =1)
Answer:
i believe that the answer is P:A if it is not I'm sorry
Step-by-step explanation:
What is the solution to the compound inequality 3x − 8 ≥ −5 and 2x − 7 < 5?
x ≤ 1 and x > 6
1 ≤ x < 6
x > 1 and x > 6
1 < x < 6
1<x<6 or its x>1 and x>6
The solution to the compound inequality is given by:
[tex]1\leq x<6[/tex]
Step-by-step explanation:The compound inequality is given by:
[tex]3x-8\geq -5[/tex] and
[tex]2x-7<5[/tex]
On solving the first inequality i.e.[tex]3x-8\geq -5[/tex]
on adding both side of the inequality by 8 we get:
[tex]3x\geq -5+8\\\\i.e.\\\\3x\geq 3[/tex]
Now on dividing both side of the inequality by 3 we get:
[tex]x\geq 1[/tex]
The second inequality is given by:[tex]2x-7<5[/tex]
On adding both side of the inequality by 7 we get:
[tex]2x<5+7\\\\i.e.\\\\2x<12[/tex]
on dividing both side of the inequality by 2 we get:
[tex]x<6[/tex]
Hence, the solution of the compound inequality is:
[tex]1\leq x<6[/tex]
Choose the graph which matches the function f(x) 2^x+2
Answer is C
If x=0, f(x) (or y) is 2^(0+2)=2²=4
So find the graph that runs through the point (0,4)
Graph C is the graph that represents the exponential function f(x) = 2ˣ⁺²
Which graph matches the function?
We want to find the graph that matches the function:
f(x) = 2ˣ⁺²
First, we can see that when x = 0 we have:
f(0) = 2² = 4
So we need to find the graph that intercepts the y-axis at y = 4. From the given options we can see a single graph that does that, which is option B, so we can conclude that B is the correct option.
what degree of rotation will cause the triangle below to map onto itself
360 is the answer for sure
Solve the equation. Round to the nearest hundredth. Show work.
[tex]4e^{5x} - e^{-x} = -3e^{2x}[/tex]
Answer:
The value of x = -0.46
Step-by-step explanation:
∵ [tex]4e^{5x}-e^{-x}=-3e^{2x}[/tex] ÷ [tex]e^{-x}[/tex]
∴ [tex]\frac{4e^{5x}}{e^{-x}}-\frac{e^{-x}}{e^{-x}}=\frac{-3e^{2x}}{e^{-x}}[/tex]
* Subtract the power of the same bases
∴ [tex]4e^{6x}-1=-3e^{3x}[/tex]
* Let [tex]e^{3x}=y[/tex]
∴ [tex]e^{6x}=y^{2}[/tex]
∴ 4y² - 1 = -3y
∴ 4y² + 3y - 1 = 0 ⇒ factorize
∴ (4y - 1)(y + 1) = 0
∴ y + 1 = 0 ⇒ y = -1
∴ 4y - 1 = 0 ⇒ 4y = 1 ⇒ y = 1/4
∵ [tex]y=e^{3x}[/tex]
∴ y = -1 refused ([tex]e^{ax}[/tex] never gives -ve value)
∴ [tex]e^{3x}=1/4[/tex] ⇒ insert ln in both sides
∵ [tex]lne^{ax}=axln(e)=ax[/tex] ⇒ ln(e) = 1
∴ 3xln(e) = ln(1/4)
∴ 3x = ln(1/4)
∴ x = [ln(1/4)] ÷ 3 = -0.46
What are the solutions to the quadratic equation 5x2 + 60x = 0?
A.) x = 0 and x = −12
B.) x = 0 and x = 12
C.) x = 5 and x = −12
D.) x = 5 and x = 12
Answer:
It's A.
Step-by-step explanation:
5x2 + 60x = 0
5x is the GCF so:
5x(x + 12 ) = 0
5x = 0, x + 12 = 0
x =0, x = -12.
Answer:
The correct option is 1.
Step-by-step explanation:
The given quadratic equation is
[tex]5x^2+60x=0[/tex]
Taking out the common factors.
[tex]5x(x+12)=0[/tex]
Using zero product property, equate each factor equal to 0.
[tex]5x=0\Rightarrow x=0[/tex]
[tex]x+12=0\Rightarrow x=-12[/tex]
The solutions of the given equations are x=0 and x=-12.
Therefore the correct option is 1.
Please answer this question, will give brainliest!
Answer:
6.63 cm
Step-by-step explanation:
The segments within the circle form a right angle. Triangle CRS as a right triangle must follow the Pythagorean theorem which says the square of each leg adds to the square of the hypotenuse.
a² + b² = c²
Here a is unknown, b = 10 and c = 12.
a² + 10² = 12²
a² + 100 = 144
a² = 44
a = √44 = 6.63
If your 5’3 and someone is 5 inches taller than you, how tall are they?
Answer:
5 foot 8
Step-by-step explanation:
Suppose y varies directly with x. If y = –4 when x = 8, what is the equation of direct variation? Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get . Solve for k to get . Write the direct variation equation with the value found for k. The equation is
Answer:
y = -1/2 x
Step-by-step explanation:
Follow the directions "Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get . Solve for k to get . Write the direct variation equation with the value found for k."
y = kx substitute y = -4 and x = 8.
-4 = k*8
-4/8 = k
-1/2 = k
So the equation is y = -1/2(x).
Answer:
1. Start with the equation of direct variation y = kx.
2.Substitute in the given values for x and y to get: -4=k(8)
3. Solve for k to get: -1/2
4. Write the direct variation equation with the value found for k. The equation is: y=(-1/2)x
Step-by-step explanation:
I just did it on e2020
select the correct slope calculation for the line that contains the points in the table.
Answer: option c
Step-by-step explanation:
By definition, you can calculate the slope of line by applying the formula shown below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Then:
You can see that in the option C the equation of the slope is applied correctly:
[tex]\frac{9-(-3)}{1-(-2)}[/tex]
Where:
[tex]y_2=9\\y_1=-3\\\\x_2=1\\x_1=-2[/tex]
Then, you obtain the following value of the slope of the line:
[tex]m=\frac{9-(-3)}{1-(-2)}=4[/tex]
Answer: Your correct answer should be C, [tex]\frac{(9 - (-3))}{(1 - (-2))}[/tex]
Step-by-step explanation:
Recall the slope equation is: (y2 - y1)/(x2 - x1) or [tex]\frac{(y2 - y1)}{(x2 - x1)}[/tex]. You need two points: point one (x1, y1) and point two (x2, y2).
* The first answer choice is flawed because not only is it in a different formula (xs are in the numerator instead of the denominator area), but it says 1 - 2 when it should be 1 - (-2) or 1 + 2.
* The second answer choice is flawed because it is in a different formula (this time, x1 - x2/y3 - y2) and 2 - 1 is suppose to be -2 - 1.
* The last answer is flawed because it should be -3 - (-) 11 and -2 - (-)4, or -3 + 11 and -2 + 4.
Note: If you had a negative operation and a negative number behind it, you can either formulate the equation like x - (-) y or drop the negative sign from said number and change the minus operation sign to the plus one (x + y).
The only answer choice that checks out and is not flawed is C.
What is the equation of the horizontal asymptote? f(x)=4(52)x+7
y=?
ANSWER
y=7
EXPLANATION
The horizontal asymptote of an exponential function
[tex]f(x)= a {(b)}^{x} + c[/tex]
is y=c.
The given exponential function is
[tex]f(x)= 4 {(52)}^{x} + 7[/tex]
When we compare to
[tex]f(x)= a {(b)}^{x} + c[/tex]
c=7, therefore the horizontal asymptote is y=7.
a 12ft ladder leans against the wall . its base us 4.5 feet from the wall. What us the angle formed by the ladder and the ground ?
pls show work!
Answer:
38.4
Step-by-step explanation:
1. Pythagorean Theorem: 4.5²+ x²= 12²→ 20.25 + x² = 144→ 144-20.25= 123.75
2. Square root 123.75, number wont be perfect, just round. (11.1)
3. Use inverse cos, sin, or tan. Answer will be the same.