Answer:
(f + g)(x) = 5x + 3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 2x - 6
g(x) = 3x + 9
(f + g)(x) is f(x) + g(x)
Step 2: Find
Substitute in function values: (f + g)(x) = 2x - 6 + 3x + 9Combine like terms: (f + g)(x) = 5x + 3Construct the 90% confidence interval for the proportion of students at the college who have completed their required English 101 course. Enter your answers as decimals (not percents) accurate to three decimal places. The Confidence Interval is
Answer:
The confidence interval has an lower limit of [tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi - 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex] and an upper limit of [tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi + 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex], in which [tex]\pi[/tex] is the sample proportion and [tex]n[/tex] is the size of the sample.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi - 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi + 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence interval has an lower limit of [tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi - 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex] and an upper limit of [tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = \pi + 1.645\sqrt{\frac{\pi(1-\pi)}{n}}[/tex], in which [tex]\pi[/tex] is the sample proportion and [tex]n[/tex] is the size of the sample.
A man invests K8 000 for 5 years at 10%p.a. compound interest.
Calculate the investment value at the end of 5 years.
Answer:
Step-by-step explanation:
Compoud interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. the formula is:
[tex]c_n=c_o(1+i)^n\\\\c_o->initial~invesment\\i->interest\\n->number~of~ intervals[/tex]
[tex]c_5=8000(1+\frac{10}{100})^5\\c_5=12848.88[/tex]
A line passes through the point (8. -8) and has a slope of
5/4
Write an equation in slope-intercept form for this line.
Answer:
y = 5/4x - 18
Step-by-step explanation:
The slope, intercept form of a straight line is;
y = bx + c
Where, y = slope, given as 5/4
(x, y) is given as ; (8, - 8)
Hence, we need to obtain the value of c, which is the intercept.
x = 8 ; y = - 8
-8 = 5/4x + c
-8 = 5/4(8) + c
-8 = 10 + c
-8 - 10 = c
-18 = c
Hence, equation becomes ;
y = 5/4x - 18
Help with number 4 I'm stuck on this algebra test with my kid and neither of us understand it
Answer:
a) x = 4
b) x = 8
c) y = -7
d) y = -10
Step-by-step explanation:
Solve by substitution on all
a)
3x + 2y = -5
3x +2 * -17/2 = -5
3x - 17 = -5
3x = -5+17
3x = 12
x = 12/3
x = 4
Plot the points (-6,8)(−6,8)left parenthesis, minus, 6, comma, 8, right parenthesis and (0,8)(0,8)left parenthesis, 0, comma, 8, right parenthesis on the coordinate plane below.
Answer:
hello I cant help you right now try again later
if △ABC = △DEF, which side is congruent to EF?
A. AB
B. BC
C. AC
Answer:
BC
Step-by-step explanation:
BECAUSE BC IT'S EQUAL TO EF
Answer:
B. BC
Step-by-step explanation:
By SSS rule in ∆ ABC and DEF,
AB = DEBC = EFCA = FDIf a equals B andB equals C which statement must be true?
Answer:
A=B=C... wouldn't both B and C be equal to A? Also I can't see the statements.
8 less than the sum of 9 and s
8 - (9 + s)
Is this it?
[tex] {x}^{2} + \sqrt{x} + \sqrt[5]{x} [/tex]
what is f'(3) of this equation?
Answer:
[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
Step-by-step explanation:
Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex] This way we could more easily use the power rule of derivatives.
So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.
f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]
to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]
A ladder is put against a building. The building is 25 feet tall. The ladder's base is 13.5 feet from the building. Find the angle which the ladder makes with the ground.
Answer:
correct me if i'm wrong but it's 57.32 degrees?
please answer only neeed solve questions
Answer:
please answer only neeed solve questions
Step-by-step explanation:
I think hlp
Answer: No question asked.
Step-by-step explanation:
If you are making a problem, please actually ask a question. It will use your points if you make questions that don't really mean anything. Thank you.
I’ll mark brainliest
Answer:
the answer is A
Step-by-step explanation:
the granpa bought 3 of the hoagie meals which means its 8×3 which is 24.
therefore he bought x of the burger meals. which means that it must be 6× X which means it is 6x.
lastly they ask for the total cost so you need to add the 24 to the 6x to get the total
¿Qué pasó en La Noche Triste?
Step-by-step explanation: La Noche Triste (Spanish for "The Sad Night") was a famous battle between the Spanish conquistadors and the Aztecs, a native people of Mexico. ... Between 400 and 800 Spanish soldiers were killed or captured. Between 2,000 and 4,000 native Mexican allies of the Spanish were killed or captured.
Location: Tenochtitlan
End date: July 1, 1520
Date: June 30
Answer: was a famous battle between the Spanish conquistadors and the Aztecs, a native people of Mexico. Between 400 and 800 Spanish soldiers were killed or captured. Between 2,000 and 4,000 native Mexican allies of the Spanish were killed or captured.
Step-by-step explanation:
If the mean of a normal distribution is 105, what is the median of the distribution? O A 315 OB. 105 O C. 420 D. 210 SUBM
Answer:
105
Step-by-step explanation:
A normal or symmetrical distribution where each the distance between each side of the distribution to the midpoint is the same, a normal distribution, also called a symmetrical distribution has the se value for both its median and mean. Hence, if the mean of a normal distribution is x, then it's median will also be x.
For the scenario given,
Since mean = 105 ; then median = 105
Can someone please help me:(
[tex]\huge\bf{\color{Green}{Question:}}[/tex]
Find the volume of each solid. Round to the nearest tenth.[tex]\huge\bf{\color{orange}{Solution:}}[/tex]
Volume of the solid given = Volume of the small cone + Volume of the large cone.
[tex]\sf{V(solid)=V(small)+V(large)}[/tex]
[tex]\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{3}π(5)²7+\frac{1}{3}π(5)²11}[/tex]
[tex]\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:=\frac{25}{3}π(7+11)}[/tex]
[tex]\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:=\frac{25}{3}π(18)}[/tex]
[tex]\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:=150π}[/tex]
[tex]\sf{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:≈{\color{magenta}{471.2 in³}}}[/tex]
=======================#Hope it helps you, mate!
(*°∀°)=3
The area of a rectangle is three times the area of a square. What is the width of the rectangle if it's length is 24 in. and the side of the square is 12 in?
Answer:
18 in
Step-by-step explanation:
Area of rectangle = 3 times the area of the square
Area of square = a² ; a = side length
a = 12 in
Area of square = 12² = 144 in²
Area of rectangle = 3 * 144 = 432 in²
Length of rectangle = 24 in
Width = x
Area of rectangle = length * width
432 = 24 * x
x = 432 / 24
x = 18 in
[tex]9x {}^{2} y {}^{3} z {}^{5} \div 6x {}^{3} yz {}^{2} [/tex]
Answer:
3y²z³ / 2x
Step-by-step explanation:
we can take one term at a time:
9/6 can be simplified to 3/2
x²÷x³ = x^-1 which equals [tex]\frac{1}{x}[/tex]
y³÷y = y²
z⁵÷z² = z³
put it all together:
3·[tex]\frac{1}{x}[/tex]·y²·z³ / 2 or
3y²z³ / 2x
pls help me do this question but pls don't get it wrong this is my last attempt
Answer:
y ≤ 5
Step-by-step explanation:
5 is the highest y value in this graph. All other y values are below 5.
Consider the following generic fixed effects model, along with a two-period (t = 1, 2), randomly sampled panel data set with dependent variable y and independent variable x: y_it = beta_0 + delta_0 d2_t + beta_1x_it + a_i + u_it where y_it = value of y for individual i at time t d2_t = binary variable equal to 1 in the second time period (t = 2), and 0 otherwise (t = l) x_it = value of x for individual i at time t a_i = unobserved (time-invariant) effect u_i = idiosyncratic error Taking the first difference of the model (that is, subtracting the regression equation for t=l from the regression equation for t=2) yields the following first-differenced equation: delta y_i = y_i2 - y_i1 = You now plan to use OLS to estimate your first-differenced equation, in order to obtain the first-differenced estimator. Suppose that delta x_i is correlated with delta u_i. True or False: The first-differenced estimator is unbiased.
A. True
B. False
Answer:
True
Step-by-step explanation:
The difference estimator is used to address the problem of omitted variables. It is used with standard fixed effects model and the data correlated is identified using regression model. The first differenced estimator used in the equation is unbiased.
City A is due north of City B. Find the distance between City A ( north latitude) and City B ( north latitude). Assume that the radius of Earth is 3960 miles.
The distance between City A and City B is ___miles.
Can someone help?! Show me step by step how this is done that I can understand it better.
=========================================================
Explanation:
The notation [tex]47^{\circ}4'[/tex] means "47 degrees, 4 minutes". The "minutes" isn't referring to a time value, but instead they are arc minutes. If we divide one degree into 60 equal pieces, then we form 60 arc minute slices. So in a sense, we are using a round analogue clock to help connect the two ideas.
We can convert to purely degrees through using this formula here
[tex]a^{\circ}b' = a + \frac{b}{60}[/tex]
So,
[tex]47^{\circ}4' = 47 + \frac{4}{60} \approx 47.06667^{\circ}[/tex]
and similarly,
[tex]22^{\circ}46' = 22+ \frac{46}{60} \approx 22.76667^{\circ}[/tex]
Now subtract the two results we got
47.06667-22.76667 = 24.3
The angular distance between the two cities is 24.3 degrees. By "angular distance" I basically mean how far you need to rotate your viewing angle when looking from city A to city B. Imagine that you're able to be situated at the center of the earth.
The circumference of the earth is
C = 2*pi*r
C = 2*pi*3960
C = 24,881.4138164311
which is approximate and the units are in miles. We multiply by the fraction 24.3/360 to find the arc distance along the curve that corresponds to the angle 24.3 degrees. This is because we don't want the whole circumference, but just a small fraction of it.
So (24.3/360)*24,881.4138164311 = 1,679.4954326091
This rounds to 1679
The distance between the two cities is about 1679 miles.
9514 1404 393
Answer:
1679 miles
Step-by-step explanation:
One minute is 1/60 of a degree, so the difference in latitudes is ...
47 4/60 -22 46/60 = 24 18/60 = 24.3 . . . degrees
The arc length is given by ...
s = rθ . . . . . . r = radius, θ = angle in radians
180° is π radians, so the surface distance between the two cities is ...
s = (3960 mi)(24.3×π/180) = 534.6π mi ≈ 1679.495 mi
The distance between City A and City B is about 1679 miles.
_____
Additional comment
As a good approximation, the distance is about 60 nautical miles per degree of latitude. Using that approximation, and converting from nautical miles to statute miles would give a distance of 1678 miles.
What conclusion can be determined from the dot plot below? A dot plot showing two dots above 6, 7, 8, 9 and 10 each. (3 points) a The number of observations is 5. b The median of the data set is 5. c The mean of the data set is 8. d The range of the data set is 8.
Answer:
C. The mean of the data set is 8.
Step-by-step explanation:
From the dot plot we can make a frequency table as follows:
Number of books read Frequency
6 2
7 2
8 2
9 2
10 2
Since, the number of dots are 10 or then sum of the frequencies is 10.
Hence, the number of observations are 10.
Also, the median of the set is: 8
Now, the mean is calculated as:
Hence, Mean of the data set is: 8
Now, the range of the data set is the difference between the minimum and the maximum value.
Hence, range=10-6=4
The range of the data set is 4.
Answer:
c
Step-by-step explanation:
Find the value of x.
Answer:
A
Step-by-step explanation:
because this shapes angle would be out of 360 so you do 360-83-85-69=123 is the answer you get.
hope it make sense:)
comment faire un patron d un prisme
Le volume d'un prisme triangulaire peut être trouvé en multipliant la base par la hauteur. Les deux images des prismes triangulaires ci-dessous illustrent la même formule. La formule, en général, est l'aire de la base (le triangle rouge dans l'image de gauche) multipliée par la hauteur, h.
Answer:
oui
Step-by-step explanation:
Can y’all help me on question 10?!
Answer: 64 square inches (choice B)
========================================================
Explanation:
Split the house shaped figure into a triangle on top and a rectangle down below.
The rectangle has area of length*width = 8*6 = 48 square inches. The 6 is from 10-4 = 6.
The triangle has area of base*height/2 = 8*4/2 = 32/2 = 16
Overall, the total area is 48+16 = 64 square inches
Health insurance benefits vary by the size of the company (the Henry J. Kaiser Family Foundation website, June 23, 2016). The sample data below show the number of companies providing health insurance for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than employees. Medium-sized companies have to employees, and large companies have or more employees. The questionnaire sent to employees asked whether or not the employee had health insurance and then asked the enployee to indicate the size of the company. Health Insurance Size of Company Yes No Total Small 33 17 50 Medium 68 7 75 Large 88 12 100 a. Conduct a test of independence to determine whether health insurance coverage is independent of the size of the company. What is the -value? Compute the value of the test statistic (to 2 decimals). The -value is - Select your answer - Using level of significance, what is your conclusion? - Select your answer - b. A newspaper article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number). Small Medium Large Based on the percentages calculated above, what can you conclude? - Select your answer -
Answer:
There is not enough statistical evidence to suggest that the health insurance coverage is independent of the size of the company
Step-by-step explanation:
The given data presented in tabular form is presented as follows;
[tex]\begin{array}{llcr}&Health \ Insurance&\\Size \ of \ Company & Yes &No &Total\\Small&34&16&50\\Medium&61&14&75\\Large&85&15&100\end{array}[/tex]
The null hypothesis, H₀; The two data are independent
The alternative hypothesis Hₐ; The variables are dependent
[tex]Expected \ value = \dfrac{(Row \ total) \times (Column \ total) }{Table \ total}[/tex]
The expected value are the values in parenthesis in the following table;
[tex]\begin{array}{llcr}&Health \ Insurance&\\Size \ of \ Company & Yes &No &Total\\Small&34(40)&16(10)&50\\Medium&61(60)&14(15)&75\\Large&85(80)&15(20)&100\\Total&180&45&225\end{array}[/tex]
[tex]\chi ^2 = \sum{\dfrac{ \left(O_i - E_i \right)^2}{E_i}[/tex]
Therefore
χ² = (34 - 40)²/40 + (16 - 10)²/10 + (61 - 60)²/60 + (14 - 15)²/15 + (85 - 80)²/80 + (15 - 20)²/20 ≈ 6.1458
The degrees of freedom = (2 - 1)·(3 - 1) = 2
The p-value from the Chi-square table is 0.05 < p-value < 0.01
Given that the p-value is larger than the significant value, we have that data is not statistically significant and we fail to reject the null hypothesis.
Therefore, the health insurance coverage is independent of the size of the company
Evaluate [315 + 6) + 2] : 7
23
O
0
03
05
Answer:
323 : 7
Step-by-step explanation:
[ ( 315 + 6 ) + 2 ] : 7
[ 321 + 2 ] : 7
323 : 7
A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 20% of the employees suffered lost-time accidents last year. Management believes that a special safety program will reduce such accidents to 10% during the current year. In addition, it estimates that 25% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
Required:
a. What percentage of the employees will experience lost-time accidents in both years?
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
Answer:
a. 5% of the employees will experience lost-time accidents in both years
b. 24% of the employees will suffer at least one lost-time accident over the two-year period
Step-by-step explanation:
a. What percentage of the employees will experience lost-time accidents in both years?
20% last year, of those who suffered last year, 25% during this year. So
[tex]p = 0.2*0.25 = 0.05[/tex]
5% of the employees will experience lost-time accidents in both years.
b. What percentage of the employees will suffer at least one lost-time accident over the two-year period?
5% during the two years.
10% during the current year. 25% of employees who had lost-time accidents last year will experience a lost-time accident during the current year.
So the 10% is composed of 5% during both years(25% of 20%) and 5% of the 80% who did not suffer during the first year.
First year yes, not on the second.
75% of 20%. So, total:
[tex]0.05 + 0.05*0.8 + 0.75*0.2 = 0.24[/tex]
24% of the employees will suffer at least one lost-time accident over the two-year period
A standard deck of 52 cards has 4 suits (spades, clubs, hearts, and diamonds) with 13 different cards (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king) in each suit. If you are dealt exactly two cards from the deck without replacement, what is the probability that you are dealt a pair (matching cards in different suits)
Answer:
P(a pair with matching cards in different suits) = 1/52
Step-by-step explanation:
We are told that there are 4 suites and each suit has 13 different cards. This is a total of 52 cards.
Thus;
Probability of selecting one card of a particular suit = 13/52 = 1/4
If we now want to select a matching card of another suit without replacing the first one, then, we now have; 52 - 13 = 39 cards. Now, there are only 3 matching cards of the 3 remaining suits that is same as the first card drawn.
Thus; probability = 3/39 = 1/13
Thus;
P(a pair with matching cards in different suits) = 1/4 × 1/13
P(a pair with matching cards in different suits) = 1/52
ABCD ~ QRST
· Find the missing side length, m
Since ABCD ~ QRST
AB/QR = AD/QT
=>6/m= 9/6
=> m = (6×6)/9 = 36/9 = 4
Answer:
m=4
Step-by-step explanation
since they are similar triangle .use these ratios
given:AB=6 , AD=9 , QR=m , QT=6
AB/QR=AD/QT
6/m=9/6
do cross multiplication
m*9=6*6
9m=36
m=36/9
m=4
therefore the value of m is 4
In parallelogram JKLM if m
Answer:
155 degree
Step-by-step explanation:
x + 25 = 180 degree (sum of adjacent angles of a parallelogram are equal)
x = 180 - 25
x = 155 degree