Solution:
Given is:
[tex]f(x) = 2x^2 - 1[/tex]
We have to find the vertex and axis of symmetry
The general equation is given as:
[tex]f(x) = ax^2 + bx + c[/tex]
Comparing with given equation,
a = 2
b = 0
c = -1
The axis of symmetry is given as:
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{0}{2(2)}\\\\x = 0[/tex]
Thus axis of symmetry is 0
The x coordinate of the vertex is the same
x coordinate of the vertex = 0
h = 0
The y coordinate of the vertex is:
k = f(h)
k = f(0)
[tex]f(0) = 2(0) - 1\\\\f(0) = 0 - 1\\\\f(0) = -1[/tex]
Thus, y coordinate of the vertex is -1
Therefore, vertex is (0, -1)
A washer and dryer cost $652 combined. The washer cost $48 less than the dryer. What is the cost of the dryer?
Answer:
The dryer costs $350
Step-by-step explanation:
Step 1: Make a system of equations
w + d = 652
w = d - 48
Step 2: Plug in the know w into the first equation
d - 48 + d = 652
2d - 48 + 48 = 652 + 48
2d / 2 = 700 / 2
d = 350
Answer: The dryer costs $350
6x+5=53 help me plzzz
Step-by-step explanation:
53-5 is 48
48/6 is 8
X=8
therefore it's 8
Answer:
x=8
Step-by-step explanation:
[tex]6x+5=53\\6x+5-5=53-5\\6x=48\\\frac{6x}{6}=\frac{48}{6} \\x=8[/tex]
what is the slope of the line shown below
Answer: 0,0 if you’re talking about the line on the see answer bar? There isn’t anything shown, but I thought I’d (somehow) help?? Sorry, mate
What is x when y = 100?
about 21
about 19
about 13
about 5
Answer:
About 13
Step-by-step explanation:
There's no equation shown, but you can guesstimate and say it's between 10 and 20, so about 13 makes sense
20 customers are eating dinner at a local restaurant. The restaurant accepts cash or credit as forms of payment. Of the 20 customers, 4 have enough cash to pay for their meal, 16 have a credit card, and 3 have enough cash and a credit card.
Using this information, answer each of the following questions. Let A be the event that a randomly selected customer has enough cash and B be the event that a randomly selected customer has a credit card.
1) What is P(A) the probability that a customer has enough cash?
2) What is P(B) the probability that a customer has a credit card?
3) What is P(A and B) the probability that a customer has enough cash and a credit card?
4) What is P(Aor B) the probability that a customer has enough cash or a credit card?
Answer:
1) P(A) = 0.20
2) P(B) = 0.80
3) P(A and B) = 0.15
4) P(A or B) = 0.85
Step-by-step explanation:
Total number of customers = 20
Customers with enough cash = 4
Customers with credit card = 16
Customers with enough cash and credit card = 3
Part 1) Customer has enough cash
Probability is defined as the ratio of favorable outcomes to total number of outcomes. Here the favorable outcome will be the customers with enough cash which are 4 in number and total number of outcomes will be the total number of customers which is 20.
Therefore, the probability that a customer has enough cash will be:
[tex]P(A)=\frac{4}{20}=\frac{1}{5}=0.20[/tex]
Part 2) Customer with a credit card
Using the same formula we used in previous part. However, in this case the number of favorable outcomes will be the number of customers with a credit card i.e. 16
Therefore, the probability that a customer has a credit card will be:
[tex]P(B)=\frac{16}{20} =\frac{4}{5} =0.8[/tex]
Part 3) Customer has enough cash and a credit card
Using the same formula once again. However, in this case the number of favorable outcomes will be the customers with enough cash and a credit card which is 3.
Therefore, the probability that a customer has enough cash and a credit card will be:
[tex]P(A \cup B)=\frac{3}{20}=0.15[/tex]
Part 4) Customer has enough Cash or a Credit Card
We need to find union of two events i.e. P(A or B). The union of two events is defined as:
P(A or B) = P(A) + P(B) - P(A and B)
We calculated all these values in the previous parts. Substituting the values in above formula, we get:
P(A or B) = 0.2 + 0.8 - 0.15
P(A or B) = 0.85
Therefore, the probability that a customer has enough cash or a credit card is 0.85
change improper fraction to mixed number
10/7
Answer:
1 3/7
Step-by-step explanation:
10/7 is same as 7/7 + 3/7
7/7 equals to 1
Therefore, 1 + 3/7
Answer: 1 3/7
Which expression could be used to determine the product of –4 and 3 and one-fourth? (negative 4) (3) times (negative 4) (one-fourth) (negative 4) (3) + (negative 4) (one-fourth) (3) (negative 4) times (3) (one-fourth) (3) (negative 4) + (3) (one-fourth)
Answer:
B.
Step-by-step explanation:
proof below
Answer:
B
it is very simple as that
In the diagram below,AB is parallel to CD. What is the value of x?
Answer: There is no diaphragm below
Step-by-step explanation: Please add picture
Find the mean, median and mode of the following data set:
Step-by-step explanation: Here, we want to find the mean, median, and mode for the data set. Let's begin by finding the mean.
The mean of a data set is equal to the sum of the set of numbers divided by how many numbers are in the set. So to find the mean of the data set shown here, let's begin by adding the numbers.
So we have
120 + 140 + 164 + 158 + 161 + 292 + 128 + 145 + 163 + 127 + 159 + 155.
This will be divided by how many numbers are in the set which is 12.
[tex]So[/tex] [tex]we[/tex] [tex]have[/tex] [tex]\frac{120 + 140 + 164 + 158 + 161 + 292 + 128 + 145 + 163 + 127 + 159 + 155}{12}[/tex].
Adding the numbers, we get 1,912.
1,912 is divided by the number of numbers in the set or 12.
1,912 divided by 12 is about 159.3333.
So the mean of the set of data shown here is about 159.3333.
Next, let's find the median.
The median is the middle number in the data set when the data set is written from least to greatest. So let's write our data set from least to greatest.
So we have 120, 127, 128, 140, 145, 155, 158, 159, 161, 163, 164, 292.
In this data set however, notice that there is no one middle number. When there is no middle number in a data set, we take the two numbers that are in the middle and we take the average of those numbers.
In this set, the two middle numbers are 155 and 158 because if we group these numbers together, there are five numbers on either side of them.
Now, to find the average of 155 and 158, we simply add them together and divide by 2. So we have 155 + 158 which is 313. Now, 313 ÷ 2 is 156.5.
So the median of the data set is 156.5.
Finally, let's find the mode.
The mode is the number that appears most frequently in a data set.
Notice that each number in our data set appears only once so there is no mode.
Answer:
120, 140, 164, 158, 161, 292, 128, 145, 163, 127, 159, 155
List the following data from least to greatest:
120, 127, 128, 140, 145, 155, 158, 159, 161, 163, 164, 292
Median: 156.5
Mode: There are no mode in the following data set.
Mean: 120 + 127 + 128 + 140 + 145 + 155 + 158 + 159 + 161 + 163 + 164 + 292 = 1,912/12 = 159.3
How many hundreds are in number 500
Answer:
5 hundreds
Step-by-step explanation:
5 is the hundreds place. So, there are 5 hundreds
Answer:
5 hundreds
Step-by-step explanation:
500 divided by 100 = 5
so, there are 5 hundreds in the number 5
19. Bella and Isaac take a weekly quiz in their
math class. Their grades on each of the ten
first quarter quizzes are shown below. Find
the difference in their mean score.
Answer:
0
Step-by-step explanation:
Because finding mean is adding the numbers, then dividing by the number of numbers. They are both 2.5. So 2.5 - 2.5 =0
Bella: 2.5
Isaac: 2.5
The difference in their mean score is 0.
What is the mean score?The mean is the arithmetic average of a set of given numbers.
Bella and Isaac take a weekly quiz in their math class.
Their grades on each of the ten first quarter quizzes are shown below.
The Bella grades are;
100, 90, 70, 80
The mean of Bella's grades is;
[tex]\rm Mean =\dfrac{Sum \ of \ all \ values}{Number \ of \ values}\\\\Mean =\dfrac{100+90+70+60}{4}\\\\Mean =\dfrac{320}{4}\\\\Mean =80[/tex]
The Isaac grades are;
100, 90, 80, 50
The mean of Isaac's grades is;
[tex]\rm Mean =\dfrac{Sum \ of \ all \ values}{Number \ of \ values}\\\\Mean =\dfrac{100+90+80+50}{4}\\\\Mean =\dfrac{320}{4}\\\\Mean =80[/tex]
The difference in their mean score is;
Difference = Bella's grades - Isaac's grades
Difference = 80 - 80
Difference = 0
Hence, the difference in their mean score is 0.
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{8x [1+(20-6)]}÷ 1/2 = ? Pls answer quick I only have 2 mins on this test!!
Answer:
60
Step-by-step explanation:
Jane thought of a number then added -5 and subtracted -8 to get 13. What number did Jane start with
PLZ HELP URGENT!!
Will award brainliest!
Ms. Zanetti receives text messages throughout her work day from her daughter’s day care provider. The possible number of text messages that she receives in a given day and the probabilities are given in the table.
Your question relates to probability in mathematics. Using various statistics techniques, we can solve these kinds of problems. However, you need to provide a specific question for further assistance.
Explanation:The subject of your problem refers to probability, which is a field of mathematics. According to the data given, we can determine or estimate the random events' likelihoods, such as Ms. Zanetti receives text messages throughout her workday from her daughter’s daycare provider, the probability of being the first in line to get a prize, or the arithmetic of random numbers for samples selection in statistics, etc.
One common way we use in probability is setting up the equation and solve it. Another method is using statistical elements, such as mean, to solve the problem. For instance, If Leah receives, on average, 6 telephone calls in two hours, and there are eight 15-minute intervals in two hours, then Leah receives on average 0.75 calls in 15 minutes.
However, your question doesn't provide me enough information to solve for a specific answer. Please provide me with the specific question, so I can assist you better.
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The probability of receiving exactly 4 text messages is 3/16.
The probability that she receives fewer than 4 text messages per day is 13/16
The probability that she receives at least 2 text messages per day is 5/8.
How to find the probability ?
To find the probability that Ms. Zanetti receives exactly 4 text messages per day, we can simply look at the probability given in the table.
Probability that Ms. Zanetti receives fewer than 4 text messages per day:
P(fewer than 4 text messages) = P(0 text messages) + P(1 text message) + P(2 text messages) + P(3 text messages)
= (1/8) + (1/4) + (3/8) + (1/16)
= (2/16) + (4/16) + (6/16) + (1/16)
= 13/16
The probability that Ms. Zanetti receives at least 2 text messages per day:
P(at least 2 text messages) = P(2 text messages) + P(3 text messages) + P(4 text messages)
= 3/8 + 1/16 + 3/16
= 6/16 + 1/16 + 3/16
= (6 + 1 + 3)/16
= 10/16
= 5/8
in the pet store, 1/6 of the puppies are black and 1/4 are white. what fraction of the puppies are black or white?
Answer:
5/12
1/6+1/4=5/12
To determine the fraction of puppies that are black or white, you add 1/6 and 1/4, which gives you 5/12 when using a common denominator of 12. Therefore, 5/12 of the puppies are either black or white.
To find out what fraction of the puppies in the pet store are black or white, we simply add the fractions that represent the black puppies and the white puppies together. Since 1/6 of the puppies are black and 1/4 are white, we can write:
[tex]\(\frac{1}{6} + \frac{1}{4}\)[/tex]
To add these fractions, we need a common denominator. The least common multiple of 6 and 4 is 12, so we convert each fraction to have a denominator of 12:
[tex]\(\frac{1}{6} = \frac{2}{12}\) and \(\frac{1}{4} = \frac{3}{12}\)[/tex]
Now, we add the fractions:
[tex]\(\frac{2}{12} + \frac{3}{12} = \frac{5}{12}\)[/tex]
Therefore, 5/12 of the puppies are either black or white.
Pls help I’ll give brainliest
Answer:
a.) 9+5x+4+8x+3
b.)13x+16
Step-by-step explanation:
Marcy’s breakfast table has a square table top with an area of 36 square feet. What is the diagonal length of the table top? how do you solve this i need help
Answer:
[tex]d=6\sqrt{2}\ ft[/tex]
Step-by-step explanation:
step 1
Find the length side of the square
we know that
The area of the square is given by the formula
[tex]A=b^2[/tex]
where
b is the length side of the square
we have
[tex]A=36\ ft^2[/tex]
substitute
[tex]36=b^2[/tex]
solve for b
[tex]b=6\ ft[/tex]
step 2
Find the diagonal length of the table top
Let
d ----> the diagonal length of the table top
Applying the Pythagorean Theorem
[tex]d^2=b^2+b^2[/tex]
substitute the value of b
[tex]d^2=6^2+6^2[/tex]
[tex]d^2=72[/tex]
[tex]d=6\sqrt{2}\ ft[/tex]
How to solve 0.5(2p+4)= -4 -2p *
Answer: p=-2
Step-by-step explanation:
0.5(2p+4)x10=-4x10-2px10
5(2p+4)=-40-20p
10p+20-20=-40-20p-20
10p=-20p-60
10p+20p=-20p-60+20p
30p=-60
30p/20=-60/30
p=-2
How can you tell which Angles are congruent from ADEF = AZXY?
Answer:
corresponding angles are listed in the same order
Step-by-step explanation:
Corresponding angles are listed in the same order in the triangle names. Corresponding angles are congruent.
∠D ≅ ∠Z
∠E ≅ ∠X
∠F ≅ ∠Y
_____
This is why you have to carefully choose the names of triangles that you say are congruent. The sequence of the letters in the name carries significant information.
x-5/50°
What is the measure of
ZQRT?
What is the value of x?
What is the measure of
ZQRS?
NEED HELP PLEASE FOR BRAINLEST
Answer:
<QRT = 130°
X = 135
<QRS = 180°
Step-by-step explanation:
1. A straight line is 180°.
180° - 50° = 130°
<QRT = 130°
2. x - 5 = 130°
130° + 5° = 135°
3. As stated before, a straight line is 180°.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the length of the hypotenuse of a right triangle whose legs are 8 and 15 units in length.
Answer:
17
Step-by-step explanation:
Pythagorean formula
a²+b²=c²
in other words, sidea²+sideb²=hypotenuse
8²+15²=c²
64+225=c²
289=c²
√289=√c²
17=c
Answer:
17
Step-by-step explanation:
Pythagorean formula
a²+b²=c²
in other words, sidea²+sideb²=hypotenuse
8²+15²=c²
64+225=c²
289=c²
√289=√c²
17=c
I need help with this one
Answer:
Step-by-step explanation:
Let w be the width
Length = w + 3
Perimeter = 40 m
2*(length + width) = 40
2*(w+3 + w) = 40
2* (2w + 3) =40
2w + 3 = 40/2
2w + 3 = 20
2w = 20-3
2w = 17
w = 17/2 = 8.5 m
w = 8.5 m
Length = w + 3 = 8.5 + 3 = 11.5m
9. James wants to purchase a telescope for
$54. If he saves $3 per week, in how many
weeks will he have saved enough to purchase
the telescope?
Answer: James will save $3 for 18 weeks before he can buy the telescope
Step-by-step explanation:
Answer:18weeks
Step-by-step explanation:
54/3=18
He will save up for 18weeks to buy the telescope
Sandy has a garden in her backyard. The drawing shows
the dimensions of her garden. A bag of fertilizer covers 3
square feet
Answer:
The answer is 12 and 4
Step-by-step explanation:
Answer:
Here is a screenshot of the finished work i've done!
Which transformations is NOT an isometry?
A.) Rotation
B.) Reflection
C.) Translation
D.) Dilation
Answer:
Dilation
Step-by-step explanation: im doing this in k-12 in math now
Dilation is NOT an isometry transformation.
We have to give that,
All the transformations are,
A.) Rotation
B.) Reflection
C.) Translation
D.) Dilation
Since, An isometry, such as a rotation, translation, or reflection, does not change the size or shape of the figure.
Dilation is not an isometry since it either shrinks or enlarges a figure.
Hence, Dilation transformations are NOT an isometry.
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Please help! 10 points!
16^x = 64^x +4
1) X =-12
2) x=-2
3) X =2
4) x=12
Answer:
Step-by-step explanation:
Enter a problem...
Algebra Examples
Popular Problems Algebra Solve for x 64^(4x)=16^(x+1)
64
4
x
=
16
x
+
1
Create equivalent expressions in the equation that all have equal bases.
4
3
(
4
x
)
=
4
2
(
x
+
1
)
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
3
(
4
x
)
=
2
(
x
+
1
)
Solve for
x
.
Tap for fewer steps...
Multiply
4
by
3
.
12
x
=
2
(
x
+
1
)
Simplify
2
(
x
+
1
)
.
Tap for fewer steps...
Apply the distributive property.
12
x
=
2
x
+
2
⋅
1
Multiply
2
by
1
.
12
x
=
2
x
+
2
Move all terms containing
x
to the left side of the equation.
Tap for fewer steps...
Subtract
2
x
from both sides of the equation.
12
x
−
2
x
=
2
Subtract
2
x
from
12
x
.
10
x
=
2
Divide each term by
10
and simplify.
Tap for fewer steps...
Divide each term in
10
x
=
2
by
10
.
10
x
10
=
2
10
Cancel the common factor of
10
.
Tap for fewer steps...
Cancel the common factor.
10
x
10
=
2
10
Divide
x
by
1
.
x
=
2
10
Cancel the common factor of
2
and
10
.
Tap for fewer steps...
Factor
2
out of
2
.
x
=
2
(
1
)
10
Cancel the common factors.
Tap for fewer steps...
Factor
2
out of
10
.
x
=
2
⋅
1
2
⋅
5
Cancel the common factor.
x
=
2
⋅
1
2
⋅
5
Rewrite the expression.
x
=
1
5
The result can be shown in multiple forms.
Exact Form:
x
=
1
5
Decimal Form:
x
=
0.2
What is A + 6 divided by 8 = 18? what is A? First to answer gets brainliest.
Answer:
A=138
Step-by-step explanation:
First you would multiply 18 times 8, which equals 144. Then you would subtract 6, which equals 138. So A=138.
Answer:
A = 138
Step-by-step explanation:
[tex] \frac{a + 6}{8} = 18 \\ a + 6 = 18 \times 8 \\ a + 6 = 144 \\ a = 144 - 6 \\ a = 138[/tex]
Suppose that of 1400 students, 550 take Spanish, 700 take biology, and 400 take both
Spanish and biology. What is the probability that a student selected at random takes
Spanish or Biology? Simplify the fraction!
Answer:
17/28Explanation:
1. Call A the event of selecting a student who takes Spanish and P(A) the corresponding probability:
P(A) = number of students who take Spanish / number of studentsP(A) = 550 / 1400 = 11/282. Call B the event of selecting a student who takes biology and P(B) the corresponding probability:
P(B) = number of students who take biology / number of studentsP(B) = 700 / 1,400 = 1/23. The joint probability, P(A∩B), is the probability that a student takes Spanish and biology:
P(A∩B) = number of students that take both Spanish and biology / number of studentsP(A∩B) = 400/1400 = 2/74. By the properties of probabilities, the probability of the event A or B is:
P (A or B) = P (A∪B) = P(A) + P(B) - P(A∩B)P(A or B) = 11/28 + 1/2 - 2/7 = (11 + 14 - 8) / 28 = 17/28Final answer:
To find the probability of a student taking Spanish or Biology, you need to consider the students taking each subject and those taking both, applying the principle of inclusion-exclusion. The simplified probability is [tex]\frac{17}{28}[/tex].
Explanation:
The probability that a student selected at random takes Spanish or Biology can be calculated using the principle of inclusion-exclusion.
Find the total number of students taking Spanish or Biology: 550 + 700 - 400 (students taking both) = 850.
Calculate the probability: P(Spanish or Biology) = Number of students taking Spanish or Biology ÷ Total number of students = [tex]\frac{850 }{ 1400} = \frac{17}{28}[/tex].
Carol has $262.10 in her bank account, and she needs to make two deposits today. One deposit is $5.30, and the other deposit is $12.30. How much money will she still have in her account after she makes her deposits?
Answer:
1,00000
Step-by-step explanation:
A scientist used 2 gallons of liquid for every 3 hours he works. He used how much of a gallon each hour he works.
Answer:
0.67 repeated or 2/3 gallons
Step-by-step explanation:
First you divide the gallons by hours because you are doing gallons per hour.
Then you get 0.66666667 and you convert that to fraction and that's your answer.
The scientist uses about 0.67 gallons of liquid for each hour of work, as per the calculation obtained by dividing the total gallons of liquid he uses (2 gallons) by the total hours he works (3 hours).
Explanation:The question here is asking how much of a gallon of liquid a scientist uses each hour if he uses 2 gallons of liquid every 3 hours. To find this, we can start by establishing the ratio of gallons to hours, which is 2 gallons per 3 hours. To find out how much of a gallon each hour he uses, we simply divide the total gallons (2) by the total hours (3).
So, to do this, we take 2 gallons ÷ 3 hours. That equals approximately 0.67 gallons per hour. Therefore, the scientist is using around 0.67 gallons of liquid for each hour he works.
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