The key features of the quadratic function are
vertex is (2, 1)Axis of symmetry: x = 2The domain of the function is the set of all real valuesDetermining the key features of the quadratic functionFrom the question, we have the following parameters that can be used in our computation:
y = -x² + 4x - 3
A quadratic function is represented as
y = ax² + bx + c
By comapring the equations, we have
a = -1, b = 4 and c = -3
For the key features
Axis of symmetry: x = -b/2a
So, we have
x = -4/(2 * -1)
x = 2
The domain of the function is the set of all real values
For the vertex, we have
(h, k) = (symmetry, f(symmetry))
So, we have
y = -2² + 4(2) - 3
y = 1
So, the vertex is (2, 1)
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Question Help About 6% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic? Assume the events are independent. (a) The probability that both will be hopelessly romantic is (Round to four decimal places as needed.)
Answer:
0.0144
Step-by-step explanation:
Answer:
Step-by-step explanation:
Both
P(both) = 6/100 * 6/100 = 36/10000 = 0.0036
At Least one
Just One
94/100 * 6/100 = 564/10000 = 0.0564
Both 0.0036
Total 0.06
Work out the size of angle A.
11 cm
9 cm
38°
Answer:
38° because the other two are cm? also you haven't linked a photo so I can't work out angle A
Help ASAP please I would love to recieve it right away
Answer:
Step-by-step explanation:
LJ/32=13/7 multiplying each side by 32
LJ=32(13)/7
LJ=416/7
LJ=59.4
Hassan sells fruits and vegetables at the marketThe mass of fruit and vegetables are in the ratio.
Fruit: vegetables = 5:7
If Hassan sells 1.33 tones of vegetables
then how many kilograms of fruits did he sell?
Answer:
950 kilograms
Step-by-step explanation:
Fruit: vegetables = 5:7
Fruit = 5
Vegetable = 7
Total ratio = 5 + 7 = 12
If Hassan sells 1.33 tones of vegetables
1 tonne = 1000 kilograms
1.33 tonnes of vegetables = 1330 Kilograms of vegetables
how many kilograms of fruits did he sell?
Let kilograms of fruits sold = x
Fruit: vegetables = 5:7
Fruit: vegetables = x : 1330
5 : 7 = x : 1330
5/7 = x/1330
Cross product
5 * 1330 = 7 * x
6,650 = 7x
x = 6,650/7
x = 950 kilograms
kilograms of fruits sold = 950 kilograms
8. Draw two circles with centre O and radii 3.6 cm and 4.5 cm, respectively. What are these
circles called?
Answer:
Concentric circles
Step-by-step explanation:
Given
Circle 1
[tex]r = 3.6cm[/tex]
Circle 2
[tex]r = 4.5cm[/tex]
Required
The name of the circles
See attachment for the circles.
From the attachment, the circle with radius 3.6cm is the circle with radius 4.5cm and they both have the same centre.
Such circles are referred to as concentric circles
2/3 of a number is 8 what is the number?
Answer:
12
Step-by-step explanation:
8/ (2/3) = 12
The value of number is,
⇒ x = 12
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
2/3 of a number is 8
Let us assume that,
A number is, x
Hence, We can formulate;
⇒2/3 of x = 8
⇒ 2/3 × x = 8
⇒ 2x = 3 × 8
⇒ 2x = 24
⇒ x = 12
Thus, The value of number is,
⇒ x = 12
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need help on edge 6th grade math
Answer: a, 7ft
Step-by-step explanation:
Answer:
Answer A
Step-by-step explanation:
Hurry I really need it I have a timer
Answer:
228 m^2
Step-by-step explanation:
I rly hope im not to late
base is 6x6=36
each side is 8x6=48
48x4=192
192+36=228
Please hurry it’s homework
Using the formula for the difference of squares, calculate: (100 - 3)
(100 + 3).
Answer:
97
Step-by-step explanation:
Answer:
Step-by-step explanation:
Explanations are below
Step 1
(100-3) Observe the equation
Step 2
(100-3) Simplify
100-(+3)
100-3
Answer: 97
Find the surface area of the figure.
Answer:
152 cm²
Step-by-step explanation:
2x5x3=30
2x6x3=36
5x6=30
2x2.5x6=30
2x6=12
(2+5)/2=3.5x2=7x2=14
30+36+30+30+12+14=152
If the total cost of a $32 item is $33.60, what is the total cost on a $55 item?
Answer:
55.00
Step-by-step explanation:
Find the amplitude and the period of the graphed function; please show work or steps.
Answers:
Amplitude = 2Period = 5pi/2===========================================
Explanation:
The lowest point occurs when y = -2. The highest point occurs when y = 2.
The vertical distance between the highs and lows is 4 units (since 2-(-2) = 2+2 = 4). This cuts in half to get 4/2 = 2.
The amplitude is 2. It measures the vertical distance from the midline to either the peaks or valleys.
-----------------------------
Note that this curve has two lowest points and one highest point shown. What we'll do is shift the graph over to the right so that each of those lowest points snap to a grid point. The lowest point on the left will move to where x = -pi, while the lowest point on the right snaps to x = 3pi/2. We'll keep each point at the same y coordinate.
The horizontal distance from x = -pi to x = 3pi/2 is
(3pi/2) - (-pi) = 3pi/2 + 2pi/2 = 5pi/2
This represents the horizontal distance from the left valley point to the right valley point. This is one full period of the curve. After we arrive at the right valley point, we repeat the process of going up and coming back down in this exact same fashion. The process is repeated forever to generate the cosine curve. The curve repeats itself every 5pi/2 units along the x axis.
Side note: any phase shift of a curve will have the same period as the original curve. This is why we're allowed to shift left or right to help find the period.
Pls help, i will give brainliest:
Consider the graphs which summarize the data on the number of hours per week of television viewing by two groups: 12-17 year-old Girls and 12-17 year-old Boys. Choose all that are correct.
The median for the girls is 16.
The median for the boys is 22.
The interquartile range for the girls is 28
The interquartile range for the boys is 16
The difference between the medians as a multiple of the IQR is 1/4
Answer:
a,b,e
Step-by-step explanation:
Answer:
B, D, E
OR
The median for the boys is 22
The interquartile range for the boys is 16
The difference between the medians as a multiple of the IQR is 1/4
Step-by-step explanation:
I just did it and got it right
Bonnie deposits 70.00 into a saving account
the account earns 4.5% simple interest per year
No money is added or removed from the savings account for 3 years
What is the total amount of money in her savings account at the end of the three years
ANSWER:
The total amount of money at the end of three years is $79.45.
Can someone help me? I’ll reward points + brainalist
Answer:
d) A = π([tex]9^{2}[/tex])
Step-by-step explanation:
area = π [tex]r^{2}[/tex]
diameter = 18
radius (half of diameter) = 9
area = π [tex]9^{2}[/tex]
In 2010, a medical research group reported the results of an experiment to evaluate the effectiveness of acupuncture to treat a chronic intestinal condition. A group of volunteers with the chronic intestinal condition agreed to participate in the experiment and be randomly assigned to either a true acupuncture treatment or a placebo treatment. The placebo treatment mimicked the application of acupuncture, but no needle penetrated the skin. Random assignment resulted in 78 subjects receiving acupuncture and 75 subjects receiving the placebo treatment. After receiving 6 treatments over the course of 3 weeks, patients were asked to report whether they had experienced a reduction in the chronic intestinal condition. The table summarizes the data from the study, with expected cell counts in parentheses. Yes No Total Acupuncture 41(37.2) 37(40.8) 78 Placebo treatment 32(35.8) 43(39.2) 75 Total 73 80 153 Which of the following is true about the chi-square test for homogeneity? A. The number of subjects randomly assigned to each treatment is not the same; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups. B. Volunteers do not constitute a random sample from the population of all patients with the chronic intestinal condition; therefore, it is not appropriate to use a chi-square test for homogeneity across treatment groups. C. Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met. D. Not all of the observed cell counts are large enough to satisfy the conditions for applying the chi-square test of homogeneity. E. Not all of the expected cell counts are large enough to satisfy the conditions for applying the chi-square test for homogeneity.
Answer: C
Step-by-step explanation:
since this was an experiment, treatments had to be randomly assigned, which satisfies the independence condition.
Answer:
ANSWER C: Volunteers with the chronic intestinal condition were randomly assigned to each treatment, so the independence condition has been met.
Step-by-step explanation:
just took the test
People with albinism have little pigment in their skin, hair, and eyes. The gene that governs albinism has two forms (called alleles), which we denote by a and A. Each person has a pair of these genes, one inherited from each parent. A child inherits one of each parent's two alleles independently with probability 0.5. Albinism is a recessive trait, so a person is albino only if the inherited pair is aa.
a. Beth’s parents are not albino, but she has an albino brother. This implies that both of Beth’s parts have type Aa. Why?b. Which of the type aa, Aa, AA could a child of Beth’s parents have? What is the probability of each type?c. Beth is not albino. What are the conditional probabilities for Beth’s possible genetic types, given this fact?
Answer:
a)
If Beth’s parents are not albino, but she has an albino brother (aa), then each parent must have the allele a. In order for someone who is not albino to be able to have an albino child of albinism, they must have type Aa.
b)
P(AA) = 0.5(0.5) = 1/4 CHANCE
P(Aa) = 0.5(0.5) = 1/4 CHANCE
P(aa) = 0.5(0.5) = 1/4 CHANCE
c)
the new probabilities are:
P(AA | not aa) = 1/3
P(Aa | not aa) = 2/3
Step-by-step explanation:
Given the data in the question;
a) Beth’s parents are not albino, but she has an albino brother. This implies that both of Beth’s parts have type Aa. Why?
If Beth’s parents are not albino, but she has an albino brother (aa), then each parent must have the allele a. In order for someone who is not albino to be able to have an albino child of albinism, they must have type Aa.
To be fully albino you must be aa and must also have at least one a as well as have a child with someone who also has has at least a.
b) Which of the type aa, Aa, AA could a child of Beth’s parents have? What is the probability of each type?
A a
A AA Aa
a aA aa
so, Since each type is equally likely, and each is inherited independently of each other then,
P(AA) = 0.5(0.5) = 1/4 CHANCE
P(Aa) = 0.5(0.5) = 1/4 CHANCE
P(aa) = 0.5(0.5) = 1/4 CHANCE
c) Beth is not albino. What are the conditional probabilities for Beth’s possible genetic types, given this fact?
First we rule out aa, since Beth is not an Albino.
the new probabilities are:
P(AA | not aa) = 1/3
P(Aa | not aa) = 2/3
2(3x - 32y) + 3(-2x - 4y)
In a class of 40 students, the number of girls is 10 more than the number of boys. We have to find the number of girls and the number of boys in the class.
Let’s represent the number of girls by g, and the number of boys by b. Write the pair of linear equations you will get in g and b :
Answer:
b=15 g=25
Step-by-step explanation:
lets translate that story problem to mathematics equations
the problem told that no. of girls are 10 more than no of boys so this will =
g=b+10
then in class there are 40 students that means
g+b=40
now we have to equations with two variables then we should substitute
(b+10)+b=40
lets remove the brackets
2b+10=40 subtract 10 from both sides
2b=30 now divide both by 2
b=15 so g=25 after you write the equation once again with the new proof or number
2X^2 - 9x + 10 . solve by factoring area model (show work)
Step-by-step explanation:
2x²_4x_5x+10
2x(x-2)-5(x-2)
(2x-5)(x-2)
I WILL GIVE BRAINLIEST :)
The two lines graphed on the coordinate grid each represent an equation
Which ordered pair represents a solution to both equations?
(1,5)
(-5,1)
(5,1)
(-1,5)
Answer:
I think it would be (1,5)
Please help me it’s due today at 11:59
Kyra is framing a square painting with side lengths of (x + 6) inches.
The total area of the painting and the frame has a side length of (2x −
5)
inches.
The material for the frame will cost $0.07
per square inch.
Complete Question:
Kyra is framing a square painting with side lengths of (x + 6) inches. The total area of the painting and the frame has a side length of (2x - 5) inches. The material for the frame will cost $0.07 per square inch.
Find the cost of the material for the frame is x = 16.
Answer:
The material cost of the frame is: $17.15
Step-by-step explanation:
Given
[tex]L_1 = (x + 6)\ in[/tex] --- Length of painting
[tex]L_2 = (2x - 6)[/tex] --- Frame and Painting
[tex]Cost = \$0.07[/tex] per square inch
Required
The cost of material of the frame
First, we calculate the area of the frame only
This is the difference between the areas of the frame and painting and the area of the painting
[tex]Area = (L_2)^2 - (L_1)^2[/tex]
[tex]Area = (2x - 5)^2 - (x + 6)^2[/tex]
Substitute 16 for x
[tex]Area = (2*16 - 5)^2 - (16 + 6)^2[/tex]
[tex]Area = (27)^2 - (22)^2[/tex]
[tex]Area = 245\ in^2[/tex]
The cost of the painting is:
[tex]Total\ Cost = Unit\ Cost * Area[/tex]
[tex]Total\ Cost = \$0.07 * 245[/tex]
[tex]Total\ Cost = \$17.15[/tex]
Hence, the material cost of the frame is: $17.15
8) A box of 12 light bulbs fell
and some are broken. If there
are 4 broken bulbs:
a) What fraction of the
bulb is broken? Write
answer in its lowest
term.
Answer: 2/3
Step-by-step explanation:
12 lightbulbs and 4 are broken
12-4=8
8/12
/2
4/6
/2
2/3
Find the errors and correct the following mathematical sentences.
something is wrong with 4th one.
I solved it as 5x.
does anyone know the answer to this? 5x-(4+3x)
Answer:
2x-4
Step-by-step explanation:
5x-(4+3x)
5x-4-3x
5x-3x-4
2x-4
A study was conducted to examine the quality of fish after seven days in ice storage. For this study Y = measurement of fish quality (on a 10-point scale with 10 = BEST.)
X = # of hours after being caught that the fish were packed in ice. The sample linear regression line is: Y = 8.5 - .5X. From this we can say that:
a. a one-hour delay in packing the fish in ice increases the estimated quality by 0.5.
b. Can't really say until we see a plot of the data.
c. a one-hour delay in packing the fish in ice decreases the estimated quality by 0.5.
d. if the estimated quality increases by 1, then the fish have been packed in ice two hours later.
e. if the estimated quality increases by 1, then the fish have been packed in ice one hour sooner.
Answer:
From this we can say that;
c. A one-hour delay in packaging the fish in ice decreases the estimated quality by 0.5
Step-by-step explanation:
The sample linear regression line representing the study of the relationship between the quality of fish, 'Y', and the number of hours that elapse after being caught that the fish were packed in ice, 'X', is presented as follows;
Y = 8.5 - 0.5·x
The estimated quality of a fish after a 1 hour delay in packaging in ice, is given as follows;
When X = 1
Y = 8.5 - 0.5 × 1 = 8.0
Therefore, the quality of a fish decreases from 8.5 to 8.0 which is equivalent to a 0.5 decrease in the quality of the fish, after a 1 hour delay in packaging in ice after being caught.
In triangle ABC, angle C is a right angle. If cos A = 5 8, what is the value of cos B?
Answer:
65
Step-by-step explanation:
In the diagram EF is the bisector of <DEF = m < D' EF.
The triangle congruence criteria that can be used to prove that DEF and D'EF are congruent is _______.
hii! i just wanted to say hope you're having a fantastic day and hope that things are going well (: stay strong and stay safe!
The triangle congruence criteria that can be used to prove that DEF and D'EF are congruent is the SAS rule.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The SAS rule states that "If two sides and the included angle of one triangle are equal to corresponding two sides and included angle of another triangle, then the triangles are congruent"
From ΔDEF and ΔD'EF
DE = D'E
m∠DEF = m∠D'EF
EF = EF
ΔDEF ≈ ΔD'EF
Thus,
The triangle congruence criteria that can be used is the SAS rule.
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