Answer:
A
Step-by-step explanation:
Answer:
D. (4,-1)
Step-by-step explanation:
So, we have these two equations:
2x + y = 7
x - 2y = 6
Isolate x in the second equation:
x = 2y + 6
Substitute it into the first equation:
2(2y + 6) + y = 7
4y + 12 + y = 7
5y + 12 = 7
5y = -5
y = -1
Plug y back into the second equation:
x - 2(-1) = 6
x + 2 = 6
x = 4
So, the correct answer is D. (4,-1)
Hope this helps!!
- Kay :)
A store sells 8 cans of fruit cocktail for $22. How much would it cost you to buy 7 cans of fruit cocktail ?
It would cost $_______
Answer:
$154
Step-by-step explanation:
Each can is $22.
You take $22x7=$154
Answer:
19.25$
Step-by-step explanation:
So first with these we always try to get the constant or divided it down to 1.
So 22 divided by 8 = 2.75, which means 2.75 is out constant.
So it is every 1 fruit cocktail it costs 2.75$.
So if we do 1 x 7 = 7
And 2.75 x 7
Then that equals 19.25
So for every 7 cans of fruit cocktail, it costs 19.25
Hope I could help.
Find the slope of the line that passes through the points (10,8) and (4,12).
WRITE THE ANSWER AS A SIMPLIFIED FRACTION PLEASE
Answer:
-2/3
Step-by-step explanation:
The formula for slope is [ y2-y1/x2-x1 ]. Use the given points to substitute and solve.
12-8/4-10
4/-6
-2/3
Best of Luck!
Answer:
\(-\frac{2}{3}\)
Step-by-step explanation:
Slope formula is:
\(\frac{y_{2} - y_{1} }{x_{2}-x_{1}}\)
Let's plug-in our numbers.
\(\frac{12 - 8}{4 - 10} = \frac{4}{-6} = -\frac{4}{6}\)
Now, we must simplify the fraction. We can do this by by finding the GCF (Greatest Common Factor). Let's list out what 6 and 4 have in common.
What can 6 be divided into?
2 * 3 = 6
1 * 6 = 6
What can 4 be divided into?
2 * 2 = 4
1 * 4 = 4
The GCF of these two numbers is 2!
\(-\frac{4\div2}{6\div2} = -\frac{2}{3}\)
So, our slope is \(-\frac{2}{3}\)
Another way to solve this is \(\frac{rise}{run}\)I have shown how to do this in the picture below. We get the same answer solving this way as well.
~ \(InLoveWithPugs\)
\(Math \ Enthusiast\\Moderator\)
a bank's monthly charge for maintaining an account is $.45 for each check written plus a service charge of $12.50. if x represents the number of checks written during the month, which function models this situation? question 4 options: f(x)
The function f(x) = 0.45x + 12.50 models the situation where a bank charges $.45 for each check written plus a service charge of $12.50. The "x" represents the number of checks written during the month.
The function that models this situation can be written as:
f(x) = 0.45x + 12.50
In this function, "x" represents the number of checks written during the month. The term "0.45x" represents the monthly charge for maintaining the account based on the number of checks written (0.45 for each check). The term "12.50" represents the service charge.
To calculate the total monthly charge, you would substitute the value of "x" into the function. For example, if you wrote 10 checks during the month, the total monthly charge would be:
f(10) = 0.45(10) + 12.50
= 4.50 + 12.50
= $17.00
In conclusion, the function f(x) = 0.45x + 12.50 models the situation where a bank charges $.45 for each check written plus a service charge of $12.50. The "x" represents the number of checks written during the month.
To know more about function visit:
brainly.com/question/31062578
#SPJ11
In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither.
Find probability that a student chosen at random has a cat or a dog.
The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.
What is probability?
Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.
Main body:
According to the question, the total number of students is; 25.
15 of them have a cat
16 of them have a dog
while, 3 of them have neither
where, x = number if students who own a cat and a dog.
Consequently, the total number of students who own a cat, a dog, both or neither is as follows;
15-x + x + 16-x + 3 = 25.
-x = 25 - 34
In essence, x = 9
the number of students who own a cat and a dog is 9.
Therefore, probability that a student chosen at random has a cat and a dog is therefore;
P(cat and dog) = 9/25.
Therefore probability that a student chosen at random has a cat or a dog is 22/25.
To know more about probability , visit:
brainly.com/question/13604758
#SPJ1
You have 7 green apples and 5 red apples. How many different, unique ways can you sort these apples keeping track of order
There are 792 different, unique ways you can sort the 7 green apples and 5 red apples while keeping track of the order.
To determine the number of different, unique ways you can sort the 7 green apples and 5 red apples while keeping track of the order, you can use the concept of permutations.
Since you have a total of 12 apples, the number of ways to arrange them can be calculated using the formula for permutations of objects with repetition.
In this case, we have 7 green apples and 5 red apples, so the formula becomes:
P(12; 7, 5) = 12! / (7! * 5!)
Calculating this expression, we get:
P(12; 7, 5) = (12 * 11 * 10 * 9 * 8 * 7 * 6) / (7 * 6 * 5 * 4 * 3 * 2 * 1) * (5 * 4 * 3 * 2 * 1)
Simplifying, we have:
P(12; 7, 5) = 792
To know more about sort refer here:
https://brainly.com/question/29257455#
#SPJ11
The following table shows the political affiliation of voters in one city and their positions on stronger gun control laws. Favor Oppose Republican 0.09 0.26 Democrat 0.22 0.2 Other 0.11 0.12 What is the probability that a voter who favors stronger gun control laws is a Republican?
The probability that a voter who favors stronger gun control laws is a Republican is 0.09 or 9%.
The probability that a voter who favors stronger gun control laws is a Republican can be found by using Bayes' theorem.
Let A be the event that a voter is a Republican and B be the event that a voter favors stronger gun control laws. Then, we want to find P(A|B), the probability that a voter is a Republican given that they favor stronger gun control laws.
Using Bayes' theorem:
P(A|B) = P(B|A) × P(A) / P(B)
P(B|A) is the probability that a voter favors stronger gun control laws given that they are a Republican, which is 0.09.
P(A) is the probability that a voter is a Republican, which is 0.09 + 0.22 + 0.11 = 0.42 (sum of Republican, Democrat, and Other probabilities).
P(B) is the overall probability that a voter favors stronger gun control laws, which is 0.09 + 0.22 + 0.11 = 0.42 (sum of Favor and Oppose probabilities for all political affiliations).
Therefore,
P(A|B) = 0.09 × 0.42 / 0.42 = 0.09
So the probability that a voter who favors stronger gun control laws is a Republican is 0.09 or 9%.
To learn more about probability here:
brainly.com/question/30034780#
#SPJ11
I need help. I don’t understand what I have to do
Answer:
Hey there!
3x-5+2x+2+3x+5
3x+2x+3x-5+2+5
8x+2=90
8x=88
x=11
Let me know if this helps :)
Step-by-step explanation:
Hey, there!!
Let's simply work with it,
MA is perpendicular to AT.
To find: angle HAT.
Now,
angle HAT + (2x + 2)° + (3x + 5)° = 90° { As MA perpendicular to AT. }
Now,
Replace angle HAT by (3x - 5)°.
(3x-5)° + (2x+2)° + (3x+5)° = 90°
Open brackets,
3x - 5° + 2x + 2° + 3x + 5° = 90°
Add like terms.
8x + 2°= 90°
8x = 90°-2°
\(x = \frac{88°}{8} \)
x= 11°.
Now, finding the value of angle HAT.
(3x-5)° = 3×11°-5°
Therefore, angle HAT is 28°.
Hope it helps...
If a system reliability of 0. 998 is required, what reliability of two components in series is required?
The reliability of two components in series is 0.996.
To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.
Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.
We can find this probability multiplying all the ten reliabilities:
P = 0.998^2 = 0.996004
Rounding to three decimal places, we have P = 0.996
The reliability of the engine is 0.996.
Hence,
The reliability of two components in series is 0.996.
Find out more information about reliability here
https://brainly.com/question/14531506
#SPJ4
Solve the following equation for x
3x-9=-33
Answer:
x = -8
Step-by-step explanation:
3x - 9 = -33
3x = -24 (add 9 to both sides)
x = -8 (divide entire equation by 3)
Answer:
x = -8
Step-by-step explanation:
Step 1: Add 9 to both sides.
3x−9+9=−33+9
3x=−24
Step 2: Divide both sides by 3.
3x -24
3 3
x=−8
How many significant digits are there in the number 6,024?
Answer:
There are four significant digits in the number 6,024.
Step-by-step explanation:
Sound waves are emitted from a fishing boat. Some of the sound waves are reflected by fish and detected back at the boat.The shortest time between the sound waves being emitted and detected is 0.26 s. The speed of sound in water is 1500 m/s.A) Calculate the distance between the boat and the nearest fish.
Answer:
195 m.
Step-by-step explanation:
The time for the sound waves to reach the fish is 0.26/2 = 0.13 seconds.
Distance = speed * time
= 1500 * 0.13
= 195 m.
y=x^2-3, what is your y value when x=4
Answer:
13
Step-by-step explanation:
4^2 is 16
16-3=13
that's all that you have to do you replace the x with 4 and do a normal equation
Answer: y=13
Y=(4)^2-3
y=16-3
y=13
what is a polygon with all sides and angles congruent
A regular polygon is a polygon with all sides and angles congruent. It exhibits symmetry and uniformity in its sides and angles, creating a visually appealing shape.
A polygon with all sides and angles congruent is called a regular polygon. In a regular polygon, all sides have the same length, and all angles have the same measure. This uniformity in the lengths and angles of the polygon's sides and angles gives it a symmetrical and balanced appearance.
Regular polygons are named based on the number of sides they have. Some common examples include the equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on. The names of regular polygons are derived from Greek or Latin numerical prefixes.
In a regular polygon, each interior angle has the same measure, which can be calculated using the formula:
Interior angle measure = (n-2) * 180 / n
Where n represents the number of sides of the polygon.
The sum of the interior angles of any polygon is given by the formula:
Sum of interior angles = (n-2) * 180 degrees
Regular polygons have several interesting properties. For instance, the
exterior angles of a regular polygon sum up to 360 degrees, and the measure of each exterior angle can be calculated by dividing 360 degrees by the number of sides.
Regular polygons often possess symmetrical properties and are aesthetically pleasing. They are commonly used in design, architecture, and various mathematical applications.
Learn more about polygon here:
https://brainly.com/question/17756657
#SPJ11
Factor each expression completely. 2 a²-16 a+32 .
The expression 2a² - 16a + 32 can be factored completely as 2(a - 4)². This means that the expression can be written as the product of 2 and the square of the binomial (a - 4).
To factor the expression 2a² - 16a + 32 completely, we can start by finding the greatest common factor (GCF) of the terms.
In this case, the GCF is 2. So, we can rewrite the expression as 2(a² - 8a + 16).
Next, we need to factor the quadratic trinomial inside the parentheses.
To do this, we look for two numbers that multiply to give us the constant term (16) and add up to give us the coefficient of the linear term (-8). In this case, the numbers are -4 and -4.
So, we can rewrite the expression as 2(a - 4)(a - 4).
However, we can simplify this further by writing it as 2(a - 4)².
To summarize, the expression 2a² - 16a + 32 can be factored completely as 2(a - 4)².
This means that the expression can be written as the product of 2 and the square of the binomial (a - 4).
know more about binomial
https://brainly.com/question/30339327
#SPJ11
.75 (x +20)=2 +0.5 (x-2)
Answer:
i need help too
Step-by-step explanation:
In right triangle XYZ, ∠Z is a right angle, m∠Y=16∘, and XZ=7. sin16∘≈0.276 cos16∘≈0.961 tan16∘≈0.287. What is the measurement of YZ?
Answer: 24.4
Step-by-step explanation:
So lets review a bit about sine, cosine, and tangent.
Look at attachment below
Okay so we have the opposite side of the triangle and are trying to find the length of the adjacent side. The only trig expression that contains both opposite and adjacent is tangent. The equation goes
tanX = opposite(XZ)/adjacent (YZ)
we know what X is X = 16
and we know what opposite is opposite = 7
so now the equation looks like
tan16 = 7/adjacent
and in the question it says that tan16 = 0.287 so lets plug that in
0.287 = 7/adjacent
0.287adjacent = 7
adjacent = 7/0.287
adjacent = 24.4
YZ = 24.4
w/2+3=5 help w/2 is a fraction Btw solve for w pleasee..!
Answer:
w = 4
Step-by-step explanation:
\(\frac{w}{2}\) + 3 = 5 ( subtract 3 from both sides )
\(\frac{w}{2}\) = 2 ( multiply both sides by 2 to clear the fraction )
w = 4
a, b, and c represent three different digits. If you add up all of the six two - digit numbers that can be written with these digits, where you don't use the same digit twice in each number, then the sum will be 528. Find these digits.
Answer:
7, 8 and 9Step-by-step explanation:
Two-digit numbers are:
ab, ac, ba, bc, ca, cbSum of them is:
10a + b + 10a + c + 10b + a + 10b + c + 10c + a + 10c + b = 52822a + 22b + 22c = 528a + b + c = 528/22a + b + c = 24The only option of three different digits with the sum of 24 is 7, 8 and 9
Answer:
The answer is 7, 8 and 9. The Two-digit numbers are: ab, ac, ba, bc, ca, cb
The Sum of them is: 10a + b + 10a + c + 10b + a + 10b + c + 10c + a + 10c + b = 528
22a + 22b + 22c = 528
a + b + c = 528/22
a + b + c = 24 The only option/options of the three different digits with the sum of 24 is 7, 8 and 9.
Hope this helps, stay safe, and merry christmas!
Joshua drops a bag of 25 chocolate chip cookies and breaks 12 of them. 100
What percentage of the cookies did Joshua break?
Answer:
48%
Step-by-step explanation:
12 out o 25 are broken
so, 12/25 = .48 * 100 = 48%
Hope this helps!
Answer:
The answer to this question is 48% is broken
Use the graph to write a linear function that relates y to x
HELP ASAP !!!!
Write and graph linear equations
Answer:
first graph the y-intercept start at 0 and go up 2 plot that. Then, go up 7 from 2 and to the right 1
Step-by-step explanation:
For the following numbers... a. Which number had the greatest frequency? 3 [ 1 point] b. What was the total sample size (n) ? 18 [1 point] c. What was the sum of the X scores ( ΣX) ? 61 [ 1 point] d. What was the sum of the squared X scores (ΣX 2
) ?
a) The number 3 has the greatest frequency. b) The total sample size is 18. c) The sum of the X scores is 61. d) The sum of the squared X scores is 145.
a. The number 3 has the greatest frequency, with 4 occurrences.
b. There are 18 numbers in the data set, so the total sample size is n = 18.
c. The sum of the X scores is ΣX = 61. This can be calculated by adding up the values of all 18 numbers in the data set.
d. The sum of the squared X scores is Σ\(X^2\) = 145. This can be calculated by squaring each of the values in the data set and then adding up the results.
To learn more about frequency here:
https://brainly.com/question/29739263
#SPJ4
Correct Question:
For the following numbers.
7 4 3 3 5 4 1 2 1
4 7 2 2 3 3 5 2 3
a. Which number had the greatest frequency?
b. What was the total sample size (n) ?
c. What was the sum of the X scores ( ΣX) ?
d. What was the sum of the squared X scores (Σ\(X^2\)) ?
Please help, I just started trig. Thanks!
Answer:
About 3.052 units
Step-by-step explanation:
I presume you won't need this explanation now, but just in case;
If we draw triangle MNK, as MN = NK we know is isosceles. Now let's draw an altitude to MK so that it splits MK into two congruent parts (5/2 = 2.5). Given M<N = 110 degrees the altitude would split the angle into two congruent angles as well (Coincidence Theorem)---- 110/2 = 55 degrees.
Now let's study the smaller triangles, and take one as an example. Remember sin(theta) = opp/hyp. Applying this we have theta as 55 degrees, the opposite side as 2.5, and the hypotenuse is yet to be found (MN);
sin(55°)= 2.5/MN,
x = 2.5/sin(55°) ≈3.052
8. an unfair coin, when tossed 7 times, has the same probability of obtaining 2 heads out of 7 as it does of obtaining 3 heads out of the 7 tosses. what is the probability the coin lands heads on a single toss?
The probability the coin lands heads on a single toss is 0.625
Let's assume that the probability of getting heads on a single toss is denoted by p.
The probability of getting 2 heads out of 7 tosses is given by the binomial distribution
P(2 heads) = (7 choose 2) × p^2 × (1-p)^5
Similarly, the probability of getting 3 heads out of 7 tosses is
P(3 heads) = (7 choose 3) × p^3 × (1-p)^4
We are given that P(2 heads) = P(3 heads), so we can set these two equations equal to each other:
(7 choose 2) × p^2 × (1-p)^5 = (7 choose 3) × p^3 × (1-p)^4
Simplifying this equation, we get
21 × p^2 × (1-p)^5 = 35 × p^3 × (1-p)^4
Dividing both sides by p^2 * (1-p)^4, we get
21/(1-p) = 35/p
Solving for p, we get:
p = 35/(21+35) = 35/56 = 0.625
Learn more about probability here
brainly.com/question/11234923
#SPJ4
Find the system of linear inequalities that corresponds to The system shown. −15x+9y
−12x+11y
3x+2y
0
−19
−18
Find all the corner points of the feasible region. (Order your answers from smallest to largest x, then from smallest to largest y.) (x,y)=(, (x,y)=(
(x,y)=(
) (smallest x-value )
(iargest x-value )
The corner points of the feasible region are:
(0, 0), (19/12, 0), (0, -19/11), and (-6, 0).
The given system of linear inequalities is:
-15x + 9y ≤ 0-12x + 11y ≤ -19 3x + 2y ≤ -18
Now, we need to find the corner points of the feasible region and for that, we will solve the given equations one by one:
1. -15x + 9y ≤ 0
Let x = 0, then
9y ≤ 0, y ≤ 0
The corner point is (0, 0)
2. -12x + 11y ≤ -19
Let x = 0, then
11y ≤ -19,
y ≤ -19/11
Let y = 0, then
-12x ≤ -19,
x ≥ 19/12
The corner point is (19/12, 0)
Let 11
y = -19 - 12x, then
y = (-19/11) - (12/11)x
Let x = 0, then
y = -19/11
The corner point is (0, -19/11)
3. 3x + 2y ≤ -18
Let x = 0, then
2y ≤ -18, y ≤ -9
Let y = 0, then
3x ≤ -18, x ≤ -6
The corner point is (-6, 0)
Therefore, the corner points of the feasible region are (0, 0), (19/12, 0), (0, -19/11) and (-6, 0).
To learn more about inequalities visit : https://brainly.com/question/25275758
#SPJ11
The length and width of a rectangle can be expressed as x+3 and x-8 . If the area of the rectangle is 60 square inches , what is the value of x?
The length and width of a rectangle can be expressed as x+3 and x-8 . If the area of the rectangle is 60 square inches , what is the value of x?
Remember that
the area of rectangle is
A=L*W
we have
L=x+3
W=x-8
substitute
A=(x+3)(x-8)
A=60 in2
so
60=(x+3)(x-8)
solve for x
x^2-8x+3x-24=60
x^2-5x-24-60=0
x^2-5x-84=0
solve the quadratic equation using the formula
we have
a=1
b=-5
c=-84
substitute
\(x=\frac{-(-5)\pm\sqrt[\square]{-5^2-4(1)(-84)}}{2(1)}\)\(\begin{gathered} x=\frac{5\pm\sqrt[\square]{361}}{2} \\ \\ x=\frac{5\pm19}{2} \end{gathered}\)the solutions are
x=12 and x=-7 (is not a solution)
therefore
the value of x is 12verifyFor x=12L=12+3=15W=12-8=4Area=15*4=60 in2 -----> is okPlz help me out ASAP!!!!!!!
Answer:
Step-by-step explanation:
A: +2
B: +2
C: -25
D: x3
scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. what is the probability that a randomly chosen test taker will score between 560 and 640?
0.8133 is the probability that a randomly chosen test taker will score between 560 and 640.
What is probability ?Probability is the possibility that something will happen, to put it simply. We can talk about the chance or likelihood of various outcomes when we don't know how an event will turn out. Events that follow a probability distribution are the subject of statistics.
Probability is a branch of mathematics that deals with numerical representations of how likely it is for an event to occur or for a proposition to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates that the event is impossible and 1 indicates certainty.
CalculationP(540< x 640)
= P ( \(\frac{560 - 560}{90}\) < \(\frac{x - mu}{sigma}\) < \(\frac{640-560}{90}\) )
By resolving this, we will obtain a probability ranging from zero to triple zero. Therefore, the likelihood will be zero. Less than zero 89 minutes our chance of being zero is zero. The values are now zero 8133 -0.5 triple zero when utilizing the table. And if we take it out, we get 0.31 33. Therefore, our likelihood of facts here ranges from 5 to 6 40. Its double three at 0.31. Therefore, this is the response to your query.
learn more about probability here :
brainly.com/question/15093426
#SPJ4
the average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents. what would the standard deviation have to be in order for a 22% probability that a gallon of gas costs less than $1.80? round z-value calculations to two decimal places and final answer to the nearest cent.
In order for a 22% probability that a gallon of gas costs less than 1.80, the standard deviation have to be 39.21 cents.
Given data,
The average retail price of gasoline (all types) for the first half of 2005 was 212.2 cents.
What would the standard deviation have to be in order for a 22% probability that a gallon of gas costs less than 1.80?Round z-value calculations to two decimal places and final answer to the nearest cent.
Method First, we have to calculate the z-value of 1.80.
Mean = 212.2 cents Standard deviation = ?
Value = 180 cents
Z = (x - μ) / σ
where, x = 180
μ = 212.2
σ = standard deviation of price distribution
Z = (180 - 212.2) / σ0.22 = P(z < (180 - 212.2) / σ)From standard normal distribution table (attached),
P(z < 0.84) = 0.7995.0.22 = 0.7995(180 - 212.2) / σσ = (180 - 212.2) / (0.22 × 0.7995)σ = 39.21 cents
Hence, the standard deviation have to be 39.21 cents in order for a 22% probability that a gallon of gas costs less than 1.80.
for such more question on probability
https://brainly.com/question/24756209
#SPJ11
ASAP someone please put these answers in scientific notation.