Answer:
x = 6
Step-by-step explanation:
2x - 5 = 7
Add 5 on both sides.
2x - 5 + 5 = 7 + 5
2x = 12
Divide both sides by 2.
2x/2 = 12/2
x = 6
New packaging for fruit snacks contains 10% less weight than the original packaging. If the new package costs 15% more than the original package, by what fraction did the unit price increase? Express your answer as a common fraction.
Answer:
5/18
Step-by-step explanation:
Let's say the original packaging was 1 lb of packaging for $1.
The cost was $1/lb.
Then the weight went down by 10% and the price went up by 15%.
Now 0.9 lb of packaging cost $1.15.
The new unit cost is $1.15/(0.9 lb)
The difference is
$1.15/(0.9 lb) - $1/lb =
= $1.15/(0.9 lb) - $0.9/(0.9 lb)
= $0.25/(0.9 lb)
=$25/(90 lb) = $5/(18 lb)
The price went up by 5/18.
Consider the following 8 numbers, where one labelled x is unknown.
11, 1, 34, x, 41, 10, 47, 2
Given that the range of the numbers is 67,
work out 2 values of x.
Answer:
x=-20 or x=68
Step-by-step explanation:
you can either make it so 47 remains the largest number and so take 67 from 47 (=-20) or you can leave 1 as the smallest number and add 67 to 1 (=68)
I'm a survey of 200 employees, 65% agreed that the management of the cafeteria should be changed. If the confidence interval is 95%, the margin of error for this survey is %, and the maximu
Answer:
Step-by-step explanation:
Confidence interval for population proportion is expressed as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
From the information given,
Sample proportion, p = 65/100 = 0.65
q = 1 - 0.65 = 0.35
n = 200
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for a confidence level of 95% is 1.96
Margin of error = 1.96√(0.65)(0.35)/200
Margin of error = 0.066 = 6.6%
The maximum boundary of the interval is
0.65 + 0.066 = 0.716
Determine the measure of the unknown angles.
PLEASE HELP!!! ASAP!!
(Picture included)
(V.O.A) means vertically opposite angle.
find the solution(s) to (x + 3)^2=49
Answer:
x = 4
x = -10
Step-by-step explanation:
(x + 3)² = 49
Take the square root of both sides.
x + 3 = ±7
The equation is x + 3 = 7 or x + 3 = -7.
x + 3 = 7
Subtract 3 on both sides.
x = 4
x + 3 = -7
Subtract 3 on both sides.
x = -10
Answer:
x₁ = -10
x₂ = 4
Step-by-step explanation:
(x + 3)² = 49
x + 3 = ± 7
x + 3 = -7 → x = -10
x + 3 = 7 → x = 4
Hope this helps! :)
Question 10 PLEASE HELP find the slope of the line described by: x-7y=-6
Answer:
slope m=1/7
Step-by-step explanation:
x-7y=-6
-7y=-x-6
y=-x/-7 -6/-7
y=1/7 x+6/7
Find m∠C. A. 16 B. 20 C. 18 D. 17
Answer:
Step-by-step explanation:
You have to use the Law of Cosines here to solve for C. For us the equation will take on the form
[tex]c^2=a^2+b^2-2abcosC[/tex] for which we have all the values except C. Filling in:
[tex]12^2=28^2+18^2-2(28)(18)cosC[/tex] which will simplify to
144 = 784 + 324 - 1008cosC. Simplify a bit more to
144 = 1108 - 1008cosC. Subtract 1108 from both sides to get
-964 = -1008cosC. Divide both sides by -1008 to get
.9563492063 = cosC
Press the 2nd button and then the cos button on your calculator. You should see this on your screen:
[tex]cos^{-1}([/tex]
After that open parenthesis, enter that long decimal and hit "enter". You should get that your angle is 16.99 which I imagine you would round to 17, which is choice D. If you did not get 16.99 but you got .29655, you are in radian mode and you need to be in degree mode. Hit "mode" and change it with your arrow key and hit "enter" and it's changed!
Which statement best describes the function below : F(x)=2x^2-3x+1
Answer:
it is a many to one function:)
Step-by-step explanation:
The statement which best describes the function F(x)=2x^2-3x+1 is it is a many to one function.
How do you find the piecewise function?
A piecewise function is a function built from pieces of different functions over different intervals. For example, we can make a piecewise function f(x) where f(x) = -9 when -9 < x ≤ -5, f(x) = 6 when -5 < x ≤ -1, and f(x) = -7 when -1 <x ≤ 9.
What is a function example?f(x) = x2 shows us that function "f" takes "x" and squares it. Example: with f(x) = x2: an input of 4. becomes an output of 16.
Learn more about piecewise function at https://brainly.com/question/27262465
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Find the measure of angle b
your answer _____
Answer:
43
Step-by-step explanation:
it looks the same as the other side
The required angle b is 43°.
It is required to find the measure of angle b.
What is angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle and corner whether constituting a projecting part or a partially enclosed space.
Given:
The measure of angle b is 43° due to vertically opposite angle.
Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other. These are sometimes called vertical angles.
Therefore, the required angle b is 43°.
Learn more details about angle here:
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Rationalize the denominator of 2/√3−1 Please give step by step answer
Answer:
√3 + 1
Step-by-step explanation:
Step below are self-explanatory
2/(√3−1)= 2×(√3 + 1)/(√3 - 1)×(√3 + 1) = multiplied both sides by √3 + 12×(√3 + 1)/(√3² - 1²)= used (a+b)(a-b)= a² - b² formula2×(√3 + 1)/(3 - 1)=2×(√3 + 1)/2= cancelled like terms√3 + 1find the difference between the endpoints of the interval on the y-axis. (1) [y-value at x=p] - (2) [y-value at x=p+k]
I know you don't need this anymore but for the ones who do this is the answer.........Look at the graph and trust it. Yes, I know it says to substitute and you can following the last page on part a) Doing what they do in the tables and it will get you the same answer as if you'd just look at the graph.
The answer for the y- value at x=p IS 8. and the answer for the y-value at x=p+k IS 5. So go ahead and write that down if you haven't already!
For step2 Find the difference between the endpoints of the interval on the y-axis. The answer to your question, Is and always will be 3! The difference is 3 because you subtract 3 from 8 and you get 5.
If you didn't read clearer, I'll write it for you again, The length interval is K, it is the length between p and p+k.
For the following questions, does your answer to step 2 depend on p, well I suppose. This is why....The answer does depend on p because we are dealing with a slope. if you move up or down the slope it will not be the same.
For the question..... Is the difference between the y-values the same regardless of where the interval starts? The answer is yes!!! And No!!! But WRITE YES! Why? Because if the interval moves as a whole the difference between the y-values is the same! Try it for yourself. Move K back two x-values and the difference for the y-values will be the same, IT WILL STILL BE THREE.
Hope you understood!
And for part one the answer on part c (-2). It depends on K.
PLEASE HELP!
Evaluate the following using exact radian measure. Show all of your work.
[tex]cot { }^{ - 1} ( - \frac{1}{ \sqrt{3} } )[/tex]
Answer:
PEMDAS DAT
Step-by-step explanation:
i need mega help quick plz
Answer:
option AAngle B is the answer
PLEASE HELP ME I REALLY NEED HELP PLEASEEEE
If a circle has an area of 12πcm² and a diameter line AB, what is the length of arc AB?
A. √3π cm
B. 3π cm
C. 2√3π cm
D. 6π cm
E. 4√3π cm
Answer:
c
Step-by-step explanation:
area of a circle = πr²
area = A²
A =√ 12π
A = 2 √ 3π
Pretty confused on finding the missing line segment. Please help.
Answer:
Option (1). 17
Step-by-step explanation:
Length of a segment having coordinates (x₁, y₁) and (x₂, y₂) is given by the formula,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Coordinates of points A and C are (4, 3) and (19, 11).
To get the length of segment AC we will substitute the coordinates in the formula,
AC = [tex]\sqrt{(19-4)^2+(11-3)^2}[/tex]
= [tex]\sqrt{(15)^2+8^2}[/tex]
= [tex]\sqrt{225+64}[/tex]
= [tex]\sqrt{289}[/tex]
= 17
Therefore, length of segment AC = 17 units.
Option (1) will be the answer.
Which number(s) below belong to the solution set of the inequality Check all that apply. x + 30 < 60 a.50 b.45 c.300 d.1 e.29 f.30
Answer:
e.29 d.1
Step-by-step explanation:
x+30<60 :we will replace with the values we have :
300 that's a big number . Obviously it isn't a solution 50 : 30+50 = 80>60 so no 45: 30+45= 75 >60 so no 30+30 = 60 we have < not ≤ so no 1 yes . it's obvious 29 +30 = 59<60 so yes !A hiker leaves camp and walks 6 miles east. Then he walks 18 miles south. How far from camp is the hiker? Distance in miles: Using quadratic applications
Answer: 19 miles
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the distance between the hiker and the camp) and a and b are the other sides.
Replacing with the values given:
x^2 = 6^2 + 18^2
x^2 = 36+324
x^2 = 360
x = √360
x = 18.97miles = 19 miles
Feel free to ask for more if needed or if you did not understand something.
Two pathways meet at 30° to each other. One pathway has lighting and the other does not.
The distance between successive lights on the lighted pathway is 5 metres. Each light has a
range of effective illumination of 6 metres.
What length of the pathway without lights is illuminated by the pathway with lights?
Answer:
12 meters
Step-by-step explanation:
Draw a picture of the two pathways 30° apart. Add a circle representing the illumination of the light on one of the pathways. Draw a line from the center of the circle to the last point where it intersects the pathway without lights.
This forms a triangle. One leg is x, the length of the pathway without lights. Another leg is 5n, where n is an integer. This represents how far the light is from where the pathways meet. The third and final leg is 6, the radius of the illumination.
Use law of cosine to solve:
6² = x² + (5n)² − 2x(5n) cos 30°
36 = x² + 25n² − 5√3 xn
0 = x² − 5√3 xn + 25n² − 36
In order to have a solution, the discriminant must be greater than or equal to 0.
b² − 4ac ≥ 0
(-5√3 n)² − 4(1)(25n² − 36) ≥ 0
75n² − 100n² + 144 ≥ 0
144 − 25n² ≥ 0
144 ≥ 25n²
144/25 ≥ n²
12/5 ≥ n
So n must be an integer less than 12/5, or 2.4. Therefore, the largest value of n is 2. Substituting:
0 = x² − 5√3 x(2) + 25(2)² − 36
0 = x² − 10√3 x + 64
Solve with quadratic formula:
x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)
x = (10√3 ± √44) / 2
x = 5√3 ± √11
x ≈ 5.34 or 11.98
We want the larger value of x. So approximately 12 meters of the pathway without lights is illuminated.
WILL MARK BRAINLIEST
help answer 4-5 please x
Answer:
Step-by-step explanation:
4. A) [tex]\frac{13}{100}[/tex]×79.50 = 10.335
tax=10.335
total cost=79.50+10.335=89.835
B) [tex]\frac{13}{100}[/tex]×189.99=24.6987 = tax
189.99+24.6987=214.6887
5) [tex]\frac{20}{100}[/tex]×544.99=108.998
yes Brittany will have enough money
A medical researcher is studying the effects of a drug on blood pressure. Subjects in the study have their blood pressure taken at the beginning of the study. After being on the medication for 4 weeks, their blood pressure is taken again. The change in blood pressure is recorded and used in doing the hypothesis test. Change: Final Blood Pressure - Initial Blood Pressure The researcher wants to know if there is evidence that the drug increases blood pressure. At the end of 4 weeks, 32 subjects in the study had an average change in blood pressure of 2.5 with a standard deviation of 4.8. Find the p -value for the hypothesis test.
Answer:
The p -value for the hypothesis test is 0.003.
Step-by-step explanation:
In this case, a paired t-test would be used to determine whether the drug increases blood pressure.
The hypothesis can be defined as follows:
H₀: The drug has no effect on blood pressure, i.e. d = 0.
Hₐ: The drug increases blood pressure, i.e. d > 0.
The information provided is:
[tex]n=32\\\bar d=2.5\\S_{d}=4.8[/tex]
The test statistic is:
[tex]t=\frac{\bar d}{S_{d}/\sqrt{n}}[/tex]
[tex]=\frac{2.5}{4.8/\sqrt{32}}\\\\=2.9463\\\\\approx 2.95[/tex]
The degrees of freedom of the test is:
[tex]df=n-1=32-1=31[/tex]
The p-value of the test is:
[tex]p-value=P(t_{31}>2.95)=0.003[/tex]
*Use a t-table.
Thus, the p -value for the hypothesis test is 0.003.
A t-test is an inferential statistic that is used to see if there is a significant difference in the means. The p-value for the hypothesis test is 0.003.
What is a t-test?A t-test is an inferential statistic that is used to see if there is a significant difference in the means of two groups that are connected in some way.
As it is given that 32(n) subjects in the study had an average change in blood pressure of 2.5([tex]\bar d[/tex]) with a standard deviation of 4.8([tex]S_d[/tex]).
Now, in order to solve the problem we need to use t-test, the test will determine whether the blood pressure increases or not under the influence of the drug.
The hypothesis for the test can be defined as:
H₀: The drug has no effect on blood pressure, therefore, d = 0.
Hₐ: The drug has increased blood pressure, therefore, d>0.
The test static is:
[tex]t = \dfrac{\bar d}{\dfrac{S_d}{\sqrt n}}\\\\\\t = \dfrac{2.5}{\dfrac{4.8}{32}} = 2.946 \approx 2.95[/tex]
Further, the degree of freedom of the test can be written as,
[tex]d_f=n-1 = 32-1=31[/tex]
Thus, the p-value of the test is:
[tex]p-value = P(t_{31} > 2.95)\\\\\text{Using the t-table}\\\\p-value = 0.003[/tex]
Hence, the p-value for the hypothesis test is 0.003.
Learn more about T-test:
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What is the value of x?
Answer:
x = 19.
Step-by-step explanation:
By the tangent - secant theorem:
BD^2 = AB * EB
so:
8^2 = (x - 7 + 4) * 4
4(x - 3) = 64
4x - 12 = 64
4x = 64 + 12 = 76
x = 76/4
= 19.
2+2 what does it 1+!
Answer:
4 AND 2
Step-by-step explanation:
Answer:
Hello!
______________________
This question is very easy.
2 + 2 = 4
1 + 1 = 2
Step-by-step explanation: Add.
Hope this helped you!
.Resolva as equações, sendo U = Q (separe as respostas por vírgulas). A) 3y - 2 = - y + 4 B) 5 - 4x = x + 3 + 2x C) - 12 - 9x = - 4 - 12x D) - x - 6 + 3x = -2x + 8x + 15
Answer:
[tex](A) y=1.5[/tex]
[tex](B)x=\dfrac27[/tex]
[tex](C)x=2\dfrac23[/tex]
[tex](D)x=-5.25[/tex]
Step-by-step explanation:
(A)
[tex]3y - 2 = - y + 4\\3y+y=4+2\\4y=6\\y=\dfrac64\\\\y=1.5[/tex]
(B)
[tex]5 - 4x = x + 3 + 2x\\5 - 4x = 3 +3x\\5-3=3x+4x\\7x=2\\x=\dfrac27[/tex]
(C)
[tex]-12 - 9x = - 4 - 12x\\-9x+12x=-4+12\\3x=8\\x=\dfrac83\\\\x=2\dfrac23[/tex]
(D)[tex]- x - 6 + 3x = -2x + 8x + 15[/tex]
[tex]2x-6 = 6x + 15\\2x-6x=15+6\\-4x=21\\x=\dfrac{21}{-4} \\\\x=-5.25[/tex]
The price of the latest John Madden PS2 gam just increased to $55 last year’s version cost $50 what is the percent increase in price? Please help
Find the area of this parallelogram
Answer:
Area = 147.03 cm²
Step-by-step explanation:
Area of parallelogram = [tex]Base*Heigth[/tex]
Where base = 16.9 cm, Height = 8.7 cm
Area = 16.9*8.7
Area = 147.03 cm²
Answer:
147.03 square cm
Step-by-step explanation:
[tex]area \: of \: parallelogram \\ = base \times height \\ = 16.9 \times 8.7 \\ = 147.03 \: {cm}^{2} \\ [/tex]
Dos familias asisten a un sitio de comidas rápidas de la ciudad, una de ellas pide 4 perros calientes y 3 hamburguesas y pagan 43000 pesos, la otra familia, piden 5 perros calientes y 1 hamburguesa y pagan 34500 pesos, se desea saber ¿cuál es el valor de cada perro y de cada hamburguesa?.
Answer:
Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.
Step-by-step explanation:
Sea x el precio de los perros calientes y y el precio de las hamburguesas.
Escribiendo los datos de la primera familia en forma de ecuación tenemos:
[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)
Escribiendo los datos de la segunda familia:
[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)
Vamos a resolver este sistema de ecuaciones por el método de suma y resta:
[tex]4x+3y=43,000\\5x+y= 34,500[/tex]
Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:
[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]
Por lo tanto, un perro caliente cuesta 5,500 pesos.
Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:
[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]
Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una
Can anyone help with this?
Answer:
115/5 23 so 20% =23 23x4 =92
Urgent ‼️50 POINTS NO BS OR I WILL REPORT YOU Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding 1/3 the length of the directed line segment?
Answer:
3rd option
Step-by-step explanation:
The ratio of 1:3 mean that one part is 1 to the other part being 3.
That means the total is 1 + 3 = 4.
1 part to 3 parts is the same as 1 part to a whole of 4 and 3 parts to a whole of 4.
Answer: 3rd option
Answer:
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Step-by-step explanation:
I like to call the numbers in the ratio 1 : 3 "ratio units".
That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).
_____
Coment on the answer wording
I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".
In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."
A chemist begins with 120 mL of a radioactive substance that decays exponentially. After 24 hours, only 30 mL of the substance remain. How many mL will remain after 48 hours? 12.5 mL 7.5 mL 4.5 mL 9.5 mL
Answer:
7.5 mL
Step-by-step explanation:
If it decays exponentially then you divide the previous number by 4 to get the next number and 30 divided by 4 is 7.5mL.
solve the equation -10x+1+7x=37
Answer:
x = -12
Step-by-step explanation:
-10x+1+7x=37
Combine like terms
-3x+1 = 37
Subtract 1 from each side
-3x+1-1 = 37-1
-3x = 36
Divide by -3
-3x/-3 = 36/-3
x = -12