To know how much each message sent costs, knowing that 75 messages cost $6.75, we only have to divide the cost of the total of 75 text messages by the total number of the cost of the message,
So that:
$ 6.75 ➗75 text message = 0.09 $/text messagesWe say, that the cost of each text message is $0.09.
Three consecutive integers have a sum of 81. Find the integers
Answer:
26, 27, 28
Step-by-step explanation:
Let the 3 integers be: x, x+1, x+2
x+x+1+x+2 = 81
3x+3 = 81
3x = 78
x = 26
x+1 = 27
x+2 = 28
You get paid an annual salary of $67,100/year. You get paid bi-
weekly. Calculate the gross pay.
Write the given transformation in vector notation (please help its due in 20 mins)
Answer:
-1, 1
Step-by-step explanation:
The translation is 1 unit left and 1 unit up.
Is it right?????????
Check the picture below.
let's bear in mind that the standard deviation measures deviation in a dataset, so is a measure of how much the data fluctuates, so a dataset of 3 , 1000, will have a much higher deviation value than a same total of 450 , 553.
Steve has a new credit card with an APR of 11.99% and a credit limit of $1800. The minimum monthly payment is 6.5 % of the new balance. If Steve buys $550 dollars in school supplies at the beginning of the month, what will Steve’s new balance be at the end of the month? Explain your answer rounded to the nearest cent
Steve's new credit card balance at the end of the month and after making the minimum monthly payment will be $519.39.
What is a credit card balance?A credit card balance is an amount the cardholder owes to the credit card issuer at the end of a credit period.
The credit card balance consists of purchases, finance charges, and repayments.
Credit card's APR = 11.99%
Credit limit = $1,800
Minimum monthly payment = 6.5%
Purchase at the beginning of the month = $550
Credit card interest for the month = $5.50 ($550 x 11.99% x 1/12)
New balance = $555.50
Minimum payment = $36.11 ($555.50 x 6.5%)
Balance after the minimum payment = $519.39 ($555.50 - $36.11)
Thus, If he buys $550 in school supplies at the beginning of the month, Steve’s new balance at the end of the month is $555.50, which he can reduce to $519.39 by making the required minimum monthly payment.
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Starting at the origin (0,0), what is the ordered pair of a value that is 4 units to the left and 5 units up?
(-4,5)
4 to the left on the axis is neg. 5 units up on the y axis makes it positive.
Pierce is making a rectangular frame for a photo collage that has a perimeter of 72.2 inches. The length of the frame is 20.3 inches.
Write an equation to find the width of the frame, x.
Enter the correct equation in the box.
An equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) = 72.2 .
As given in the question,
Pierce is making a rectangular frame for a photo collage.
Perimeter of a rectangular frame is equal to 72.2 inches.
Length of the rectangular frame is equal to 20.3 inches
Perimeter of the rectangle = 2(length + width) __(1)
Let x inches be the width of the frame
Equation with x width of the frame is given
2(20.3 + x) = 72.2
Therefore, an equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) =72.2.
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Use the diagram find the image of c under the translation described by the translation rule
(X,y) (x+11,y-8)
○ B
○ A
○ D
○ E
Given the following Information, find the length of the missing side. Leave your answer as a simplified radical.
Hypotenuse = 10
Long = ?
A. 5
B. 5/3
C. 10
D. 10/3
Answer: B. (5√3)
Step-by-step explanation: In a 60-30-90 triangle, the hypotenuse is 2x, and the long is x√3. Solve for x by setting 2x=10, which you would get 5. Then, you can plug 5 for x in x√3 to get 5√3.
3.4-2.8d+2.8d-1.3Combine like terms to create an equivalent expression.
The given expression is
3.4 - 2.8d + 2.8d - 1.3
By collecting like terms, we have
- 2.8d + 2.8d + 3.4 - 1.3
= 0 + 2.1
= 2.1
A scientist is working with two different concentrations of hydrochloric acid (HCI). One bottle is
80% HCI, and the other is 50% HCI. For their experiment they need 1 liter of 70% HCI.
How many liters of the 80% solution do they need?
How many liters of the 50% solution?
The liters of 80% material is 2/3 liters.
The liters of the 50% solution is 1/3 liters.
How to illustrate the information?Based on the information, the scientist is working with two different concentrations of hydrochloric acid (HCI).
Let x = volume of 80%
Let 1 -x =volume of 50%
Therefore, the expression to illustrate the information will be:
80x + 50 × (1 - x) = 70
80x + 50 - 50x = 70
30x = 70 - 50
30x = 20
Divide
x = 20/30
x = 2/3
Therefore there are 2/3 liters of 80% material
The liters for the 50% solution will be 2/3 subtracted from 1. The 2/3 implies that for the 80% material. This will be:
= 1 - 2/3
= 1/3
There are also 1/3 liters of 50% material.
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Kara categorized her spending for this month into four categories: Rent, Food, Fun, and Other. The amountsshe spent in each category are pictured here.Food$289Rent$361Other$433Fun$217What percent of her total spending did she spend on Rent? Answer to the nearest whole percent.
Total expenses = $289 + $361 + $433 + $217 = $1300
Percentage of money spent on rent:
(Money spent on rent)/(Total expenses) = $361/$1300 = 0.2777 ≈ 28%
Therefore 28% of total expenses are for rent
30% of 3000
I know how to do it but I just need to be sure
Answer:900
Step-by-step explanation: 1. set up an equation
x= (p * n)/100 when x= the answer p= the percentage and n= the total number
2. plug in the numbers
x= (30 * 3000)/100
3.solve
x= (30*3000)/100
x= (90000)/100
x= 900
circle C has centre D and equation
x^2+y^2+2x-8y+8=0
A line is drawn through the point P (4,6),so that it touches the circle C at the point T
Show that PT=square root 20
find the equation of the circle centre P which passes through the point T
The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Here, we are given a circle with center D and equation as-
[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]
Comparing this to the general form of equation of a circle which is [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-
g = 1, f = -4 and c = 8
thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3
Now, since PT is a tangent to the circle, DP will e perpendicular to PT.
We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)
= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]
= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]
= [tex]\sqrt{25 +4 }[/tex]
=[tex]\sqrt{29}[/tex]
Thus, in triangle, PDT by using Pythagoras theorem, we will have-
[tex]PT^{2} + DT^{2} = PD^{2}[/tex]
since DT is the radius of the circle, DT = 3
⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]
[tex]PT^{2} + 9 = 29[/tex]
[tex]PT^{2} = 29 - 9[/tex]
[tex]PT^{2} = 20[/tex]
[tex]PT = \sqrt{20}[/tex]
Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.
Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]
so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)
Thus, the equation of the circle will be-
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]
[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]
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Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, and Nyberg, 2004). In a typical study, a researcher
obtains a sample of n = 16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general popula-tion, scores from the test form a normal distribution with a mean of μ = 50 and a standard deviation of σ = 12. The sample of research participants had an average of M = 54. a. Assuming a two-tailed test, state the null hypoth-esis in a sentence that includes the two variables being examined.
b. Using the standard 4-step procedure, conduct a two-tailed hypothesis test with α = .05 to evaluate the effect of the supplements
Using the z-distribution to test the hypothesis, we have that:
a) The null hypothesis is [tex]H_0: \mu = 50[/tex].
b) The p-value of the test is greater than 0.05, hence we do not reject the null hypothesis, meaning that the supplements did not have the intended effect.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the mean was different, hence:
[tex]H_0: \mu = 50[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean was different, hence:
[tex]H_1: \mu \neq 50[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In the context of this test, the parameters are given as follows:
[tex]\overline{x} = 54, \mu = 50, \sigma = 12, n = 16[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{54 - 50}{\frac{12}{\sqrt{16}}}[/tex]
z = 1.33.
What is the p-value and what is the conclusion?Considering a two-tailed test, as we are testing if the mean is different of a value, with z = 1.33, the p-value of the test is of 0.1835, which is greater than 0.05, meaning that we do not reject the null hypothesis and the supplement did not change the mean.
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P
TU =
UV =
32°
-
5.5 cm
3.1 cm
VW-
Tech Support
151°
S
cm
cm
Q
Look carefully at quadrilateral PQRS.
Consider the transformation Rz (PQRS) that produces its image, quadrilateral
TUVW.
Find all the following:
cm
147°
3.8 cm
6.0 cm
30°
R
N
Answer:
Step-by-step explanation:
Your cousin gave you $13.78 with which
to buy a present. This covered 2/3 of the
cost. How much did the present cost?
The cost of the present is $20.67
Given,
The cost of the present = x
Amount given by cousin = $13.78
Amount given by cousin is 2/3 of x.
That is,
13.78 = 2/3 of x
Lets find x
13.78 = 2/3 × x
13.28 = 2x/3
Multiply with 3 on both sides
13.78 × 3 = (2x/3) × 3
We get,
41.34 = 2x
Divide 2 on both sides
That is,
41.34/2 = 2x/2
We get,
x = 20.67
Here, x is the cost of the present
Therefore, the cost of the present is $20.67
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write a quadratic function in standard form containing the point (5,-6) and x-intercepts -7 and 3
WILL GIVE BRAINLIEST
Answer:
[tex]y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]
Step-by-step explanation:
Intercept form of a quadratic equation
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-intercepts.a is some constant.Given:
x-intercepts: -7 and 3Point on the curve: (5, -6)Substitute the given values into the formula and solve for a:
[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies-6&=a(5-(-7))(5-3)\\-6&=a(12)(2)\\-6&=24a\\a&=\dfrac{-6}{24}\\\implies a&=-\dfrac{1}{4}\end{aligned}[/tex]
Substitute the given x-intercepts and the found value of a into the formula:
[tex]\implies y=-\dfrac{1}{4}(x+7)(x-3)[/tex]
Expand to standard form:
[tex]\implies y=-\dfrac{1}{4}(x^2-3x+7x-21)[/tex]
[tex]\implies y=-\dfrac{1}{4}(x^2+4x-21)[/tex]
[tex]\implies y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]
list 3 points that are on the line 2x=6y+4
The three Points that lie on the given line 2x=6y+4 are (5,1) , (8,2) and (11,3).
The given equation of line is given below,
2x=6y+4 equation 1
We need to find the points that lie on the given line.
Point 1 :
Put x = 5 in equation 1
2(5) = 6y + 4
6y = 6
y=1
So, Point (5,1) lie on the given line.
Point2:
Put x = 8 in equation 1
2(8) = 6y + 4
6y = 12
y=2
So, Point (8,2) lie on the given line.
Point 3 :
Put x = 11 in equation 1
2(11) = 6y + 4
6y = 18
y=3
So, Point (11,3) lie on the given line.
Thus, Points (5,1) , (8,2) and (11,3) lie on the line 2x=6y+4 .
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If f(x) = 3x - 1 and g(x) = x + 2, find (f- g)(x).
A. 3-2x
B. 4x+1
C. 2x-3
D. 2x-1
Blake was assigned the problem below. Analyze his work and determine if it is correct.If it is wrong, describe all mistakes.Problem:53x-5 = ( 625 )#*?53x-s5 "(x+2)3x-5 = 4 (x+7)3x-5= 4x+7-3x-3xS = x +7-7-7x= -12
1) Let's solve that exponential equation
Converting the bases:
2) Since we are on the same base let's just calculate the exponents.
3) Blake has committed a mistake when He didn't apply the distributive property properly. He didn't multiply the 7 by 4. He subtracted the x variables wrongly and added -7 to -5.
When He started operating the exponents.
uppose that the rela
S={(-1, -9), (-9, 1), (3, 1)}
ve the domain and range of S.
rite your answers using set notation.
domain =
range =
Help me please
Answer:
Domain = {-9, -1, 3}Range = {-9, 1}Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
The depth of a local lake averages 26 ft, which is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|. What is the difference between the depths in February and July?
21 feet
23 feet
8 feet
13 feet
The difference between the depths in February and July is D. 13 feet.
How to illustrate the information?From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.
Therefore, it should be noted that the depth in July is -18.
Therefore, the difference between the depths in February and July will be:
= -5 - (-18)
= -5 + 18
= 13
Therefore, the difference is 13 feet.
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Which conversion factors can be used to multiply to 4 km/min to get meters per hour?Select each correct answer. 1 km1000 m1 h60min60min1 h1000 m1 km
Step 1: Concept
To convert km to meters you will multiply with 1000.
To convert minute to hour you will divide by 60
Step 2: Convert
[tex]\begin{gathered} 4\operatorname{km}\text{ to meters = 4 }\times\text{ }\frac{1000m}{1\operatorname{km}}\text{ } \\ 1\text{ min to hour = 1}\min \times\frac{1\text{hour}}{60\text{ min}} \end{gathered}[/tex]Step 3: Final answer
[tex]\frac{1000m}{1\operatorname{km}}\text{ and }\frac{1hour}{60\min }[/tex]Option B and D
A garden table and a bench cost $830 combined. The garden table costs $80 more than the bench. What is the cost of the bench?
The most appropriate choice for linear equation will be given by-
The cost of bench is $375
What is linear equation?
A one degree equation is called a linear equation.
Here,
Let the cost of the bench be $x
cost of garden table = $(x + 80)
Total cost of bench and garden table= $(x + x + 80)
= $(2x + 80)
By the problem,
2x + 80 = 830
2x = 830 - 80
2x = 750
x = [tex]\frac{750}{2}[/tex]
x = $375
So,
The cost of bench is $375
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Help me answer this please!!!
Answer:2 choice
Step-by-step explanation:you use the rise over run technique with 2 points, it should give you rise 1 run 4 since the line is decreasing its a negative. For the y-int its the point where the line crosses Y int which is (0,-2) answer is -2
given a number line C=11 and D=13 CD=?can u help me solve this problem?
The diagram of the number line is shown below
Thus, the distance CD which is the distance between point D and point C is
13 - 11 = 2
CD = 2
find the value of k given both points lie on a line passing through the orgin (-12,-2) and (k,8)
The value of k given that both points lie on a line passing through the origin is 48.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Since both points lie on a line which passes through the origin, we can logically deduce the following points:
Point (x, y) = (0, 0)
Substituting the given points into the formula, we have;
Slope, m = Δy/Δx
Slope, m = (-2 - 0)/(-12 - 0)
Slope, m = -2/-12
Slope, m = 1/6
At point (-12, -2) and (k, 8), we have:
1/6 = (8 - (-2))/(k - (-12))
1/6 = (8 + 2)/(k + 12)
1/6 = 10/(k + 12)
k + 12 = 10(6)
k + 12 = 60
k = 60 - 12
k = 48
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10. A blood alcohol content (BAC) of 0.08 g/100 mL means
please solve the inequality in the picture shown below i will give brainliest
[tex]\frac{3}{4} -\frac{1}{2} p > \frac{5}{4} \\\frac{3}{4}(4)-\frac{1}{2} p(4) > \frac{5}{4} (4)\\3-2p > 5\\-2p > 5-3\\-2p > 2\\\frac{-2p}{-2} > \frac{2}{-2} \\p < -1[/tex]
when you divide or multiply by a negative number the signs <> change directions.