Eric had $197 in his savings account before he was paid his weekly salary. His current savings balance is $429. How much money does Eric earn each week? (Form an equation.)
Answer:
[tex]197+\text{ n= 429}[/tex]Explanation:
Here, we want to get the amount of money Eric earns per week
Let the amount earned be n
Now, to get the value earned, we have to subtract the value he had before from what he has now or simply add what he had before to what he earned now and equate to his total balance now
Mathematically, we have that as:
[tex]197\text{ + n = 429}[/tex]Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the difference. Write your answer in simplest form.
The expression of the fraction 10¹/₅ - 2¹/₆ as a mixed fraction is; 8¹/₃₀
How to subtract Fractions?We want to subtract two fractions.
Now, fractions could be either proper fraction, improper fraction or mixed fraction.
Now, a proper fraction simply means the numerator is smaller than the denominator, a mixed fraction simply means a whole number and a proper fraction while an improper fraction simply means the numerator is bigger than the denominator
We are given the operation;
10¹/₅ - 2¹/₆
Converting to improper fraction gives;
51/5 - 13/6
Factorizing gives us;
1/30((51 * 6) - (13 * 5))
= 241/30
Converting to mixed fraction gives 8¹/₃₀
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Using the graph as your guide, complete the following statement.
The discriminant of the function
• A. positive
• B. negative
• C. zero
=======================================================
Reason:
The discriminant is
d = b^2-4ac
which is the stuff under the square root in the quadratic formula.
We have these three cases
d > 0 means we get two different real number solutionsd = 0 means we get exactly one real number solutiond < 0 means there are two nonreal complex solutionsThe graph shows we have 2 solutions. Each solution is an x intercept, aka "root". We go for the case in which d > 0. Therefore, the discriminant is positive.
He is able to jog 600 meters every minute, keeping a constant speed. After jogging for 8 minutes, he stops to have a drink of water. If he has to jog 9,700 meters to get to work, then what should his constant pace be if he has no more than 15 minutes to get to work? Helppp
Based on the distance that has to be jogged to get to work, and the current speed, the constant pace that is needed to get to work is 327 meters per minute
How to find the constant pace?First, find out how much of the journey has already been jogged:
= Meters per minute x Number of minutes
= 600 x 8
= 4,800 meters
Distance left to get to work:
= 9,700 - 4,800
= 4,900 meters
The constant pace can be found by the formula for speed:
= Distance / time
= 4,900 / 15 minutes
= 327 meters per minute
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15) tan 330°2नउ16) tan 135°3Use the given point on the terminal side of angle to find the value of the trigonometricfunction indicated.17) tan18) sinLave(4,2√5)10,-11)
The trigonometric ratios of an angle represented with its terminal side are given by the following equations:
[tex]\begin{gathered} tanθ=\frac{y}{x} \\ sinθ=\frac{y}{\sqrt{x^2+y^2}} \end{gathered}[/tex]The first angle terminal side is located at (10, -11), then we get:
[tex]tanθ=\frac{-11}{10}=-\frac{11}{10}[/tex]Similarly, for the second angle:
[tex]\begin{gathered} sinθ=\frac{2\sqrt{5}}{\sqrt{(2\sqrt{5})^2+4^2}}=\frac{2\sqrt{5}}{\sqrt{4\times5+16}}=\frac{2\sqrt{5}}{\sqrt{20+16}}=\frac{2\sqrt{5}}{\sqrt{36}}=\frac{2}{6}\sqrt{5}=\frac{\sqrt{5}}{3} \\ sinθ=\frac{\sqrt{5}}{3} \end{gathered}[/tex]2. A line goes through the points (4, 8) and (-4, 6). (a) What is the slope of the line? Show your work (b) Write the equation of the line in point-slope form. Show your work (c) Write the equation of the line in slope-intercept form. Show your work. Answer:
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 52.4 for a sample of size 25 and standard deviation 8.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level). Assume the data is from a normally distributed population.
Enter your answer as a tri-linear inequality accurate to three decimal places.
answer < μ < answer
The patient's systolic blood pressure will be lowered by 48.709< m<56.091 at a 98% confidence interval.
What is a confidence interval?
For an unknown parameter, a confidence interval is just a range of guess. Usually 95% confidence level is generally the most usual, but other levels, such 90% or 99%, are occasionally used to generate a Confidence interval.The reduction in systolic blood pressure is, mean, x=52.4
Sample size, n=25
Standard deviation, s=8.5
We must determine the t value for a 90% Confidence interval because the sigma is unknown.
From Inverse t Distribution Calculator, the Confidence interval is 0.98 and the degree of freedom is 25-1=24:
One-sided t-Score: 2.1715
We can now determine the standard error E:
E=2.1715(8.5/√25)=3.691
We can now create the confidence interval by:
x - E < m < x+ E
52.4-3.691< m<52.4+3.691
48.709< m <56.091
The patient's systolic blood pressure will be lowered by 48.709< m <56.091 at a 98% confidence interval.
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Susan is painting her living room. Two of the walls are 10.75 feet long and 7 feet tall, and two of the walls are 6.875 feet long and 7 feet tall. If half a gallon of paint covers 200 square feet, how much paint will Susan need?
Answer:
2.63903744 gallons of paintStep-by-step explanation:
Check image below for explanation
If .5 gallon covers 200
and Susan needs 246.75
1 whole gallons covers 400 (too much)
.5 gallon = 200 paint
?? gallon = 46.75 paint
200 / 46.75 = 4.27807487
.5 / 4.27807487 = 2.13903744
2.13903744 gallon = 46.75 paint
So,
.5 gallon+ 2.13903744 gallon = 2.63903744 gallons
(200 paint + 46.75 paint = 246.75 paint)
2.6 gallons (rounded)
Melissa will only drink a cup of coffee if she has slept less than 8 hours or she had to wake up before 6
am.
In which of the following cases does Melissa not drink a cup of coffee?
Melissa sleeps for 8 hours and wakes up at 7 am
Melissa sleeps for 7 hours and wakes up at 8 am
Melissa sleeps for 9 hours and wakes up at 5:30 am
Melissa sleeps for 7 hours and wakes up at 6 am
Check
W
Answer: Melissa sleeps for 8 hours and wakes up at 7 am.
Step-by-step explanation: For this i was able to do just eliminate some answer. "Melissa sleeps for 7 hours and wakes up at 8 am," in this case Melissa would drink coffee because she slept less than 8 hours. "Melissa sleeps for 9 hours and wakes up at 5:30 am," in this case Melissa would drink coffee since she had woke up at 5:30 am. "Melissa sleeps for 7 hours and wakes up at 6 am," in this case Melissa would drink coffee since she had less than 8 hours of sleep. In conclusion, The only time Melissa wouldn't had drank coffee is when she had slept for 8 hours and woke up at 7 am. That is because had slept more than 8 hours and had woke up after 7 am.
What should be done to both sides of the equation in order to solve 1/3 x=4? Divide by 4Multiply by 4 Divide by 1/3Multiply by 1/3
The given equation is,
[tex]\frac{1}{3}x=4[/tex]So, from this equation , we have to find the value of x. The left hand side of the equation has x with 1/3 as coefficient, therefore, inorder to make it x, we have to,
[tex]\frac{1}{3}x\times3\rightarrow x[/tex]as the thress get cancelled. If we do some operation on one side of the equal sign, it is to be applied on the other side also so as to maintain the equivalency.
So here we have to multiply by 3.
But in option, there is no as such given , but it is given that divide by 1/3.
[tex]\frac{\frac{1}{3}x}{\frac{1}{3}}\rightarrow\frac{1}{3}x\times3^{}^{}[/tex]which is equuivalent to multiplying by three.
So the option " Divide by 1/3" is correct.
Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF, which intersect at I. If DI = 3, BD = 4, and BI = 8, then find the area of triangle ABC.
The area of a triangle is 1/2 x base x height.
The area of a triangle is 24.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices
The area of a triangle is given by:
Area = 1/2 x base x height
We have,
A triangle ABC.
Angle bisectors are AD, BE, and CF, which intersect at I as shown in the figure below.
DI = 3
DI = AI = 3
Height of the triangle = AD = AI + DI = 3 + 3 = 6
BD = 4 = BC
Base of the triangle = BC = BD + DC = 4 + 4 = 8
The area of a triangle:
= 1/2 x base x height
= 1/2 x 8 x 6
= 1 x 4 x 6
= 24
Thus,
The area of a triangle is 24.
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whats the answer for this question
Answer:
Step-by-step explanation:
12-2=10
9+7-10=6
Only brother: 9-6=3
Only Sister: 7-6=1
Both:6
In ∆XYZ, y =75cm, z=83 cm and
we have:
[tex]undefined[/tex]
3. Jake purchased 6 packages of burgers for $53.76. Each package contains 8 burgers. How
much did Jake pay for 1 burger?
Answer:
$1.12
Step-by-step explanation:
x = 8
6x = 53.76
6(8) = 53.76
48 burgers = 53.76
Divide 53.76 by 48 for cost per burger (53.76 ÷ 48)
Does the following graph depict y as a function of x?
in this problem
the graph define a function, because the x-value has only one output (one value of y)
Write the following inequalities in interval notation. Type “infinity” for infinity. A) c_<1 B) x<1.6 C) x_>9/2
Answer:
Explanations
Inequalities expressions are expressions not separated with an equal sign. The inequality signs are <, >, ≤ and ≥.
From the given question, we are to write the given inequality in interval notation.
Interval notation are represent using the set notation symtion sym
Simplify the expression.[tex] - 5 {w}^{4} {y}^{ - 2} \div - 15 {w}^{ - 6} {y}^{2} [/tex]w≠0, y≠0
Question:
Simplify the expression
[tex]\frac{-5w^4y^{-2}}{-15w^{-6}y^2},w\ne0,y\ne0[/tex]Step 1:Apply the fraction rule
[tex]\begin{gathered} \frac{-a}{-b}=\frac{a}{b} \\ \frac{-5}{-15}=\frac{1}{3} \end{gathered}[/tex][tex]\frac{-5w^4y^{-2}}{-15w^{-6}y^2}=\frac{w^4y^{-2}}{3w^{-6}y^2}[/tex]Step 2:Apply the law of indices
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex][tex]\frac{w^4y^{-2}}{3w^{-6}y^2}=\frac{w^{4-(-6)}y^{-2-2}}{3}[/tex][tex]\begin{gathered} \frac{w^{4-(-6)}y^{-2-2}}{3} \\ =\frac{w^{4+6}y^{-4}}{3} \\ =\frac{w^{10}y^{-4}}{3} \end{gathered}[/tex]Step 3: Apply the fractional exponent of indices
[tex]a^{-m}=\frac{1}{a^m}[/tex][tex]\begin{gathered} \frac{w^{10}y^{-4}}{3} \\ =\frac{w^{10}}{3}\times\frac{1}{y^4} \\ =\frac{w^{10}}{3y^4} \end{gathered}[/tex]Hence,
The final answer = w¹⁰/3y⁴
The nature of a graph which has an odd degree and a negative leading coefficient would be _________.up left; up rightdown left; up rightdown left; down rightup left; down right
Given:
A graph which has an odd degree and a negative leading coefficient.
To find:
The nature of the graph.
Explanation:
Since the has an odd degree and a negative leading coefficient.
So, the end behaviours are,
[tex]\begin{gathered} As\text{ }x\rightarrow-\infty,f(x)\rightarrow\infty \\ As\text{ }x\rightarrow\infty,f(x)\rightarrow-\infty \end{gathered}[/tex]So, the nature of the graph would be, up left and down right
Final answer:
up left; down right.
After how many days do only 4/5 of the students recall the important features of the classroom lecture? There are two parts to this questionIt says locate the point on the graph that conveys this information
Given:
[tex]P(x)=90-25log_2x[/tex]Required:
We need to find the value of x when P(x)=80.
Explanation:
[tex]Substitute\text{ P\lparen x\rparen=80 in the equation }P(x)=90-25log_2x.[/tex][tex]80=90-25log_2x[/tex]Solve for x.
[tex]25log_2x=90-80[/tex][tex]25log_2x=10[/tex]Divide both sides by 25.
[tex]\frac{25log_2x}{25}=\frac{10}{25}[/tex][tex]log_2x=\frac{2}{5}[/tex][tex]Use\text{ If }log_bx=y\text{ then }b^y=x.\text{ here b=2 and }y=\frac{2}{5}.[/tex][tex]x=2^{\frac{2}{5}}[/tex][tex]x=2^{0.4}[/tex][tex]x=1.3\text{ days.}[/tex]Final answer:
[tex]x=1.3\text{ days.}[/tex]See a horizontal line from point 80 on the y axis and mark the intersection point on the graph.
lfp 3.1/ 3.2 practice
Divide fractions
3.1/3.2
PART 1,
Pithagorean theorem
x^2 =™9^2 + 12^2 = 81 + 144 = 225
then
x=√225 = 15
PART 2
x^2 = 10^2 + 24^2 = 100 + 576 = 676
then
x= √676 = 26
PART 3
10 ^ 2 = x^2 + 6^2
So then
10^2 - 6^2 = x^2
100 - 36 = x^2
64 = x^2
√64 = 8 = x
PART 4
24^2 = x^2 + 6^2
So then write
24^2 -6^2 = x^2
576 - 36 = x^2
As a result
540 = x^2
Then
√540 = x
Which of the following are geometric sequences?Check all that apply.A.2, -2, 2, -2, 2, -2, 2B.1, 2, 4, 8, 16, 32C.1, 4, 9, 16, 25, 36, 49D.10, 5, 2.5, 1.25, 0.625, 0.3125
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The correct answers are:
CONCLUSION:
The final answers are:
OPTION B and OPTION D
For the following, I have to find where the orthocenter, the centroid, and the circumcenter are within the diagram
Orthocenter
Let
A(2,0)
B(3,2)
C(6,0)
step 1
Find out the slope AB
m=(2-0)/(3-2)
m=2/1
m=2
Remember that
If two lines are perpendicular, then, their slopes are negative reciprocal
so
the slope of the altitude that passes through C is -1/2
Find out the equation of the altitude that passes through C
y=mx+b
we have
m=-1/2
point C(6,0)
substitute
0=-(1/2)(6)+b
solve for b
0=-3+b
b=3
equation is y=-(1/2)x+3 -------> equation 1
step 2
Find out the slope BC
m=(0-2)/(6-3)
m=-2/3
so
the slope of the altitude that passes through A is 3/2
Find out the equation of the altitude that passes through A
y=mx+b
we have
m=3/2
point A(2,0)
0=(3/2)(2)+b
solve for b
0=3+b
b=-3
y=(3/2)x-3 ------> equation 2
step 3
the intersection point equation 1 and equation 2 is the orthocenter
y=-(1/2)x+3 -----> equation 1
y=(3/2)x-3 ------> equation 2
solve the system
solve by graphing
using a graphing tool
the intersection point is (3,1.5)
that means
the orthocenter is (3,1.5)
see the attached figure to better understand the problem
HELP ON Q1 Q2 AND Q3, WILL GIVE BRAINLIEST IF U HELP ME
The simplified expressions for each case are given as follows:
1 - a) 11g.
1 - b) 3m.
1 - c) -k².
2 - a) 8x + 11y.
2 - b) 2a + b - 2c.
3 - a) 5q + 7.
3 - b) 6r + 3s + 7t.
How to simplify an expression?An expression is simplified combining the like terms, that is, adding or subtracting, depending on the signal, the terms that have the same variable and the same exponent.
For item 1, the variables are common for all terms, hence we just add the terms keeping the variable, hence:
4g + 6g + g = 11g.4m - m = 3m.5k² - 4k² - 2k² = -k².For item 2, there are multiple variables, hence we combine the terms of each variable(we cannot add terms with x and y, for example), as follows:
5x + 3x + 5y + 6y = 8x + 11y.2a + 4b + 6c - 3b - 8c = 2a + b - 2c.Item 3 works similarly to item 2, as there are multiple variables, hence we combine the terms with each variable(or with the constant = no variable), as follows:
9q - 4q + 15 - 8 = 5q + 7.8r + 2s + 4t - 2r + s + 3t = 6r + 3s + 7t.What is the missing information?The questions are missing and are given by the image at the end of the answer.
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Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?
x squared + x + 1 + StartFraction 2 Over x + 1 EndFraction
x squared minus x + 1
x squared + x + 1 + StartFraction 2 Over x minus 1 EndFraction
x cubed minus x squared + x minus 1
The quotient is equal to [tex]x^{2} +x+1[/tex]
Given
The provided equation is as follows:
[tex]\frac{x^{2}+1 }{x-1}[/tex]
What exactly is synthetic division
The synthetic division method is a quick way to divide polynomials.
When divided by the linear factor, it is also known as the polynomial division technique of a specific instance.
Therefore,
The quotient is as follows:
[tex]\frac{x^{2}+1 }{x-1}[/tex]
[tex]\frac{x(x^{2} +x+1)-1(x^{2} +x+1)}{x-1}[/tex]
[tex]\frac{(x-1)(x^{2} +x+1)}{x-1}[/tex]
[tex]x^{2} +x+1[/tex]
As a result, the quotient is
[tex]x^{2} +x+1[/tex]
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Answer: C
Step-by-step explanation:
The president of the student council wants to survey the student population about parking. She decides to take a random sample of 100 of the 1,020 students at the school. She gets an alphabetical list of the students, and numbers them from 0001 to 1020. Then, using a random number table, and starting at a random line, she selects 100 unique numbers between 0001 and 1020. Is this a simple random sample?
No, because the sample could contain repeating numbers.
No, because the sample could contain numbers other than numbers between 0001 and 1020.
Yes, because each student and sample of 100 has the same chance of being selected.
Yes, because each student is represented by a 4-digit number from 0001 to 1020.
Is this a simple random sample: Yes, because each student and sample of 100 has the same chance of being selected.
What is a simple random sample?A simple random sample can be defined as a subset of items that are selected from a larger data set or statistical population, with each member of the subset having an equal or the same probability (chance) of being selected.
This ultimately implies that, each member of the subset are selected by chance and randomly, and as such a simple random sample is an unbiased representation of a larger data set or a statistical population.
In this context, we can reasonably infer and logically deduce that the data set or statistical population described in this scenario is a simple random sample.
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There are 8 grams of pure drug in 75 milliliters of solution. What is the precent strength of solution? Round tothe nearest hundredth
Step 1: Let's review the information given to us to answer the exercise correctly
Amount of pure drug in the solution = 8 grams
Amount of solution = 75 mL
Step 2: Let's answer the question, as follows:
Percent strength of the solution = Amount of pure drug in the solution/Amount of solution * 100
Replacing with the values we know:
Percent strength of the solution = 8/75 * 100
Percent strength of the solution = 0.10666 * 100
Percent strength of the solution = 10.67% (Rouding to the next hundredth)
Tenth = one decimal place
Hundreth = two decimal places
Thousandth = three decimal places
7 1/2 X 2 X 3
Help asap please
Answer:
Hey! So basically, 7 1/2 x 2 = 15 and 15 x 3 = 45
Hope this helped! :D
A bag has 5 blue marbles and 10 green marbles. Half of the green marbles are made of glass. A marble is selected at random from the bag. What is the probability that it is a green, glass marble
Answer:
1/3Step-by-step explanation:
Total marbles:
5 + 10 = 15Green marbles made of glass:
10/2 = 5Required probability:
P(green glass) = 5/15 = 1/3According to the Housing Recommendations, if a family has a gross annual income of $52,000, what is the maximum amount of a mortgage loan the family could afford?
State your answer in terms of dollars, but do not include a $ sign or the word "dollars" with your response.
Given m/8= 86° and m/4= (4x + 2)°, what is the value of x ?
m∠4=m∠8 (Corresponding angles are equal)
[tex]4x+2=86\\4x=86-2\\4x=84\\\frac{4x}{4} =\frac{84}{4} \\x=21[/tex]
x=21°