Answer: [tex]5x^{2}-4[/tex]
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)=4x^{2}+1+x^{2}-5=\boxed{5x^{2}-4}[/tex]
A coin is tossed, and a die is rolled. What is the probability that the outcome is a head or an even number?
Answer: When a coin is tossed and a die is rolled the probability of getting a head or an even number is = 3/4
Step-by-step explanation:
probability : The ratio of the favorable outcome to the total outcomes is gives the probability.
So for the given case all possible outcomes are = 12(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)
total no of outcomes when there is head on coin are = 6(1,H),(2,H),(3,H),(4,H),(5,H),(6,H)
Total no of outcomes when there is even on dice are = 3(2,T),(4,T),(6,T)
So the total number of favorable outcomes are:6+3 = 9
Total outcomes = 12Therefore the probability is given by 9/12 = 3/4
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Answer: The probability of getting a head or an even number is = 3/4
What is probability?It is the measure of how likely an event or outcome is. Different events have different probabilities!For the given case: Possible outcomes are(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)
So, no. of possible outcomes 12
No. of coin outcomes (when it's head) = 6(1,H),(2,H),(3,H),(4,H),(5,H),(6,H)
No of dice outcomes (when it's even) = 3(2,T),(4,T),(6,T)
So the total number of favourable outcomes are:6+3 = 9
Total outcomes = 12
Probability = [tex]\frac{No. of favorable outcomes}{total outcomes}[/tex]
Probability for this case is = [tex]\frac{9}{12} =\frac{3}{4}[/tex]
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Calculate the number of two-person committees that can be formed from a group of 10 people
Bikash borrowed Rs150,000 from Anish at the rare 21% per year at the end of 9 month. How compound interest should he pay compound half yearly.
The factors of 25x4 − 49y2 are
Answer:
1
Step-by-step explanation:
49 is divisible by 7, 1, 49. 25 is divisible by 5, 1, 25. they are exclusively prime so the highest factor is 1 and the only
Answer:
Step-by-step explanation:
[tex]25x^4-49y^2=(5x^2)^2-(7y)^2\\=(5x^2+7y)(5x^2-7y)\\=(5x^2+7y)[(\sqrt{5} x)^2-(\sqrt{7y} )^2]\\=(5x^2+7y)(\sqrt{5} x+\sqrt{7y} )(\sqrt{5} x-\sqrt{7y} )[/tex]
2) An electronic gadgets distributor distributes various brands of mobiles to retailers.
The data for the number of smartphones distributed in nine months (Jan-Sep) are
collected to make a box-and-whisker plot. Read the plot and answer the questions.
H
20
30
40
a) Write the median from the above given plot.
b) What is the least number of smartphones distributed?
c) Write the third quartile from the given plot.
50
t>
60
The median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.
What is the box and whisker plot?A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a box and whisker plot shown in the picture.
From the box plot, the line between the box ends represents the median of the data.
The median = 40
The least number of smartphones distributed = 33
Q3 = 48
Thus, the median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.
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What is the solution to the inequality StartFraction d Over 7 EndFraction + 4 ≤ 0? (–∞, –28) (–∞, –28] (28, ∞) [28, ∞)
The solution to the inequality d / 7 + 4 ≤ 0 will be (–∞, –28]. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality equation is given below.
d / 7 + 4 ≤ 0
By simplifying the equation, we have
d / 7 ≤ – 4
d ≤ – 28
Then the value of d must be less than or equal to the negative 28.
Then the correct option is B.
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On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value? Find the t-table here. t = –1.85; the P-value is 0.9678. t = –1.85; the P-value is between 0.025 and 0.05. t = 1.85; the P-value is 0.9678. t = 1.85; the P-value is between 0.025 and 0.05.
Using the t-distribution, the correct option regarding the test statistic and the p-value is given as follows:
t = –1.85; the P-value is between 0.025 and 0.05.
What are the hypothesis tested?
The null hypothesis is:
[tex]H_0: \mu = 25[/tex]
The alternative hypothesis is:
[tex]H_1: \mu < 25[/tex]
What are the test statistic and the p-value?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In this problem, the values of the parameters are given as follows:
[tex]\overline{x} = 23.5, \mu = 25, s = 4.8, n = 35[/tex]
Hence the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{23.5 - 25}{\frac{4.8}{\sqrt{35}}}[/tex]
t = -1.85.
Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.
Hence the correct statement is:
t = –1.85; the P-value is between 0.025 and 0.05.
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someone help solve asap for points
Answer:
[tex]\textsf {p(-4) = -134}[/tex]
Step-by-step explanation:
[tex]\textsf {Given :}\\[/tex]
[tex]\mathsf {p(x) = x^{3} - 3x^{2} + 7x + 6}[/tex]
[tex]\textsf {Substitute x = -4 to find p(-4) :}[/tex]
[tex]\mathsf {p(-4) = (-4)^{3} - 3(-4)^{2} + 7(-4) + 6}[/tex]
[tex]\mathsf {p(-4) = -64 - 48 - 28 + 6}[/tex]
[tex]\textsf {p(-4) = 6 - 140}[/tex]
[tex]\textsf {p(-4) = -134}[/tex]
Match each quadratic equation with its roots.
a2-a+11=0
a2-2a+15=0
a = 1ti√14
1± √47
a= 2
a=
1+√43
2
a=1+3i
a2-2a+10=0
a2-a+12=0
30
Answer:
wrong question please place correctly thanks
Solve based off of the screenshot provided below.
Answer:
48 cm²
Explanation:
The figure can be cut into 1 rectangle and 1 triangle.
Area of the figure:
⇒ area of rectangle + area of triangle
⇒ Length × Width + 1/2 × Base × Height
⇒ 6 × 4 + 1/2 × 6 × 8
⇒ 24 + 24
⇒ 48
Therefore, area of figure is 48 cm².
Answer:
48 cm squared
Step-by-step explanation:
The given figure is composed of a rectangle (L=6 cm and W = 4 cm) and a right angled triangle { Base = (12- 4) = 8 cm, height = 6 cm. }
Area of the two figures is to be calculated separately and then added to get the required result.
Area of the rectangle = l × w
= 6 × 4
= 24 cm²
Area of the right triangle = ½ × base × height
= ½ × 8 × 6
= 24 cm²
Hence, area of the given figure = 24 + 24
= 48 cm squared.
(07.01) A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours?
Answer: By 8 hours, there will be 65536 bacteria in the culture.
Step-by-step explanation:
The numerical expression used for this problem is [tex]4^{8}[/tex].
You can find the value of this on a calculator. I hope this helps!! :)
If that is not the answer, then try 32 because 4*8=32.
A tank weighs 5.6kg when it 1/4 filled with water.If it weighs 10.4kg when it is full ,what will be it's weight when it is empty.
Answer:
4 kg
Step-by-step explanation:
so 1.6 * 4 is 6.4 so you just double check if you want
4 + 1.6 which is 1/4 of 6.4 will be 5.6 (matches with the question)
4 + (1.6*4) (indicates it's full) = 10.4( also Matches with the question)
there is another way by setting up an equation. let me know in comments if you want to see it that way
If tank weighs 5.6kg when it 1/4 filled with water. If it weighs 10.4kg when it is full , then weight when it is empty is 0.93kg
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A tank weighs 5.6kg when it 1/4 filled with water
Tank weighs 10.4kg when it is full
We need to find the weight when it is empty.
Let weight of the tank “x” and the weight of the water in the full tank “y”.
From the problem statements, we deduce the following equations:
x + y/4 = 5.6kg => x = 5.6kg - y/4
x + y = 10.4kg => y = 10.5kg - x
y = 10.5kg - (5.6kg - y/4)
3y/4 = 4.9
Thus y = 6.53kg; x = 0.93kg
Hence, weight of the tank when it is empty is 0.93kg.
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Find the measure of PR.
The length of PR = 18 .
What is a Chord ?A chord is a line segment whose both points lie on the circle.
When a chord is extended it is called secant .
When two chords meet outside the circle , the product of length of the secant and its external segment is equal to the product of length of other secant and its external segment.
According to the given data
FR and FP are the secants of the circle
To determine the measure of PR
From the secant theorem
(7+9) * 9 = (5x+8) * 8
16 * 9 = (5x+8) *8
2 *9 = 5x+8
18 = 5x+8
5x = 10
x = 2
Therefore the length of PR = 5x+8 = 10+8 = 18
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Compute the length of sides AB, AC.
Karen runs 7 miles in 50 minutes. At the same rate, how many miles would she run in 75 minutes?
Answer :
10.5 miles
Given :
7 miles in 50 mins
Step-by-step explanation :
Calculate how many miles in 1 minute :
Divide both by 50 :
7/50 miles in 1 minute
To work out 75 minutes we multiply both by 75 :
75 × 7/50 =
10.5
Therefore our final answer is 10.5 miles
Hope this helped and have a good day
Solve the following triangle. Round side measure to the nearest tenth and angle measure to the nearest degree:
Answer: [tex]AB=4.7, BC=8.8, \angle C=28^{\circ}[/tex]
Step-by-step explanation:
As angles in a triangle add to 180 degrees,
[tex]\angle C=180^{\circ}-90^{\circ}-62^{\circ}=\boxed{28^{\circ}}[/tex]
We know that:
[tex]\sin 62^{\circ}=\frac{BC}{10}\\\\BC=10\sin 62^{\circ} \approx \boxed{8.8}[/tex]
Similarly,
[tex]\cos 62^{\circ}=\frac{AB}{10}\\\\AB=10\cos 62^{\circ} \approx \boxed{4.7}[/tex]
PLEASE HELP IF YOU DO YOU BELIEVE IN JESUS THANK YOU SO MUCH
These steps outlined were used to construct the perpendicular bisector of
Answer: ZT = ZS
Step-by-step explanation: ZT = ZS must be true under all circumstances. This is because a perpendicular bisector of a line cuts the line into two equal pieces. It is the midpoint of the entire line. Thus, ZT is the same as ZS since the line is equally cut in half and thus are the same.
The square of the difference between a number and 7 is 81 . Find the number(s).
Answer:
16 or -2
Step-by-step explanation:
Let the number be x.
Difference between the number and 7
= x -7 or 7-x
The square of the difference between x and 7
= (x -7)²
(x -7)²= 81
Square root both sides:
[tex]x - 7= \pm \sqrt{81} [/tex]
[tex]x - 7 = \pm9[/tex]
Add 7 to both sides:
[tex]x = 7\pm9[/tex]
x= 16 or x= -2
Thus, the number could either be 16 or -2.
A student needed to find the measure of angle b. She incorrectly said mZb=118°. Find the correct measure of angle b. What mistake did she likely make?
Answer:
D
Step-by-step explanation:
To find angle B, you should subtract 62 from 90 since because a right angle is 90 degrees.
What is the common difference in the following arithmetic sequence?
2.8, 4.4, 6, 7.6, ...
–4.8
–1.6
1.6
4.8
Answer:
1.6
Step-by-step explanation:
4,4-2.8 = 1.6
6-4.4 = 1.6
7.6-6 = 1.6
Then common difference is 1.6
Which expression is equivalent to One-fifth (150 x minus 80 y + 50 minus 50 x minus 25 y + 20)?
20 x minus 21 y + 14
20 x + 11 y + 14
20 x minus 11 y + 6
20 x + 21 y + 6
Answer:
150 x - 80 y + 50 - 50 x - 25 y + 20
Arranging like terms
150 x - 50 x -25 y - 80y + 50 + 20
100x - 105 y + 70
5 ( 20x - 21y + 14)Answer:
20x - 21y + 14
Explanation:
[tex]\rightarrow \sf \dfrac{1}{5} (150x - 80y + 50 - 50x - 25y + 20)[/tex]
collect like terms
[tex]\rightarrow \sf \dfrac{1}{5} (150x-50x - 80y -25y + 50 + 20)[/tex]
add/subtract like terms
[tex]\rightarrow \sf \dfrac{1}{5} (100x - 105y+70)[/tex]
distribute inside parenthesis
[tex]\rightarrow \sf \dfrac{1}{5} (100x) + \dfrac{1}{5}( - 105y) + \dfrac{1}{5}(70)[/tex]
simplify the following
[tex]\rightarrow \sf 20x -21y + 14[/tex]
) The correlation between a car’s engine size and its fuel economy (in mpg) is r= -0.774. What fraction of the variability in fuel economy is accounted for by the engine size?
The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.
Given that, r= -0.774.
To solve such problems we must know about the fraction of the variability in data values or R-squared.
What fraction of the variability in fuel economy is accounted for by the engine size?The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.
It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r” in a simple regression model.
Fraction of the variability in data values = (coefficient of correlation)²= r²
Now, the variability in fuel economy = r²= (-0.774)²
= 0.599076%= 59.91%
Hence, the fraction of the variability in fuel economy accounted for by the engine size is 59.91%.
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Ethan is following a healthy diet plan and is allowed 3000 calories and 30 grams
of fat a day.
He is trying to decide what to have for his lunch.
Chicken
Sandwich
Nutrition Facts
Energy
Protein
Carbohydrate
Sugar
Fat
Fibre
Sodium
per pack
265 kcal
36 g
15 g
2g
6g
1.2 g
476 mg
Jacket potato
with tuna
Nutrition Facts
Energy
Protein
Carbohydrate
Fat
Saturated Fat
Fibre
Sodium
per 1 serving
450 kcal
30 g
75 g
79
19
9.1 g
432 mg
a) If he chooses a chicken sandwich what percentage of his daily allowance of fat
will that be?
06
Why can’t 1.07 pounds of sugar be compared to 1.23 cups of sugar.
What type of polynomial is P(x)=2+x?
Answer: linear polynomial
Step-by-step explanation:
f(x) = -3 +3
Which graph represents the inverse of function ?
-3
N
-1
4
3-
2-
1-
-2+
-3-
-4+
-5+
W.
Y
54
-1-
4-
3-
2
-4
-2
N
-3
-5+
X.
Y
4-
3-
2-
-1-
3
X
e
Answer: Y
Step-by-step explanation:
Since f(x) passes through (0,3), its inverse should pass through (3,0).
This eliminates X and Z.Also, since f(x) has a negative slope, so its inverse should also have a negative slope.
This eliminates W.The graph of the inverse of function is shown in figure.
We have to given that,
Function is defined as,
f (x) = - 3x + 3
Hence, The inverse of function f (x) is,
f (x) = - 3x + 3
y = - 3x + 3
Solve for x,
3x = y + 3
Divide by 3;
x = (y + 3) / 3
Hence,
f⁻¹ (x) = (x + 3) / 3
f⁻¹ (x) = x/3 + 1
Therefore, The graph of the inverse of function is shown in figure.
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How do I find dy/dx of the following?
Answer:
[tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]
Step-by-step explanation:
[tex]y \ = \ x^{3} \ - \ \displaystyle\frac{1}{\sqrt{x}} \ + \ \displaystyle\frac{3}{x^{4}} \\ \\ y \ = \ x^{3} \ - \ x^{-\frac{1}{2}} \ + \ 3x^{-4} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{3 \ - \ 1} \ - \ \left(-\displaystyle\frac{1}{2}\right)x^{-\frac{1}{2} \ - \ 1} \ + \ \left(-4 \ \times \ 3\right)x^{-4-1}[/tex]
[tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2}x^{-\frac{3}{2}} \ - \ 12x^{-5} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]
Select the correct answer.
What is the solution to this equation?
log(2x - 100) = 3
A = 1,000
B = 450
C = 550
D = 100
Suppose we want to choose 7 colors, without replacement, from 9 distinct colors
If the order of the choices does not matter, how many ways can this be done?
The number of ways to choose the colors is 36
How to determine the number of ways?The given parameters are:
Colors = 9
Colors to choose = 7
Since order does not matter, then it is combination
This is calculated using:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^nC_r = \frac{9!}{7!2!}[/tex]
Evaluate
[tex]^nC_r = 36[/tex]
Hence, the number of ways is 36
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4+0.4+0.0024 in Standard Form
Answer:
In standard form thats 4.4024
In standard form, 4+0.4+0.0024 can be written as 4.4024
Concept: Any number we can write as a decimal number, between 1.0 and 10.0, multiplied by 10, is said to be in the normal range. 1.23 × 108;
If you look closely, 1.23 is a decimal number between 1.0 and 10.0 so we have a standard form 123,000,000 as 1.23 × 108.
Given: 4+0.4+0.0024
In this case,4 is the integral value and 0.4 is at the first decimal place followed by 0.0024 at the third and 4th decimal place so combining them all together and writing them in standard form we get,4.4024
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Sandra owns a rectangular pice of farmland that is 2/3 miles wide and has an area 5/9 square mile what is the leght of sandras farmalnd
Answer:
5/6 mile
Step-by-step explanation:
The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.
__
Here is the equation for the area of a rectangle.
A = LW . . . . . area is the product of length and width
When we fill in the area and width, we have ...
5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland
Solving this equation gives ...
L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L
L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division
The length of Sandra's farmland is 5/6 mile.
