We are given the following expression:
[tex]7(6t+2)+3-5(t-1)[/tex]To simplify the expression, we will first use the distributive property on the parenthesis, like this:
[tex]7\times6t+7\times2+3-5\times t+5\times1[/tex]Solving the operations:
[tex]42t+14+3-5t+5[/tex]Now we add like terms:
[tex](42t-5t)+(14+3+5)[/tex]Solving the operations:
[tex]37t+22[/tex]This is the most simplified form of the equation
what number is not part of the solution set for the inequality below?3x-18> 1210, 11, 15,8 _
First, let's solve for x in the inequality to find an interval, the options that are not included in the interval are not part of the solution set, we can do it by following these steps:
1. 3x-18> 12 , add 18 on both sides:
3x - 18 + 18 > 12 + 18
3x > 30
2. Divide both sides by 3:
3x/3 > 30/3
x > 10
So, to be a part of the solution, x must be greater than 10, then the interval that represents the solution is (10, ∞). From the given options, the only one that is not included in this interval is 8, because it is less than 10, then the answer is 8.
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
Step-by-step explanation:
h = number of hours
s = number of shirts made
28h+2s=144
4h=s
h=4, s=16
(Didn't I already answer this? i think i might have.. lol)
I have a question for quantitative reasoning. Alcohol use by high school seniors in a certain state decreased from 50.3% in 2000 to 32.7% in 2015. Describe this change as an absolute change in terms of percentage points and as a relative change in terms of a percentage.
The of senior high school students who reported consuming alcohol is mathematically given as
33.99% of
This is further explained below.
What percentage of senior high school students report consuming?Absolute change is the straightforward difference between the indicator's two time periods.
Absolute change = final value - initial value
Absolute change =(33 *1-50.3)% points
=-17.2% points
Decrease absolute change $=17.2% point
- ve hours decreased
+ve shows increased
The percentage of high school seniors using alcohol decreased by 17.2%. point
Relative change expresses absolute change as the ax of the value in the initial period
[tex]$=\frac{\text { absolute change }}{\text { intial value }} \times 100$$=\frac{33.1-50.3}{50.3} \times 100$[/tex]
=-33.99 %
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A manufacturing machine has a 4% defect rate.
If 9 items are chosen at random, what is the probability that at least one will have a defect?
The probability that at least one will have a defect is 19%.
What is probability?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.
p = 4% = 0.04
q = Prob of a defective product is 0.03; hence, Prob(non-defective) = 1 - 0.04 = 0.96.
Prob(at least one flaw) is now equal to 1 - Prob (0 defects)
= 1 - 9C0 x 0.04^0 x 0.96^9
= 1 - 1 x 1 x 0.815
= 0.19 or 19%
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Determine the intercepts of the line
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
Since the number of years must be non-negative, we can eliminate all the options except for d.
What is the rate of return when 12 shares of Stock
A, purchased for $22/share, are sold for $465? The
commission on the sale is $9.
Rate of Return = profit or loss
total cost
First, calculate the total cost.
Hint: 12 shares were purchased for $22
each. So first, we'll multiply 12 - 22.
12- $22= $[?]
The rate of return of the 12 shares purchased by A is 72.72%.
Here, we are given that A purchases 12 shares at $22 per share.
So the cost price of 12 shares will be = 12 × 22
= 264
A sold these shares at $465.
The commission on sale = $9.
Thus, the total cost of the shares will be = 264 + 9
= $273
Hence, the total profit of A will be-
465 - 273
= 192
The rate of return is calculated as-
Rate of return = profit/cost price × 100
Thus, here-
Rate of return = 192/264 × 100
= 0.7272 × 100
= 72.72%
Thus, the rate of return on these 12 shares purchased by A is 72.72%.
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i only need help with 12 & 13 only and show work please. note the picture is sideways
Answer:
12. 65:6 = 65/6 = 65 to 6
13: 21:4 = 21/4 = 21 to 4
Step-by-step explanation:
You want the numerical values of the given ratios of blood donors written three ways.
In each case, replace the blood type with the corresponding number of donors. Ratios can be written using a colon, a division bar, or the word "to".
12. A+ and B+ to AB+Using the numbers, this is ...
(45 +20) : 6 = 65 : 6 = 65/6 = 65 to 6
13. A- and B- to AB-Using the numbers, this is ...
(21 +0) : 4 = 21 : 4 = 21/4 = 21 to 4
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
55.17
Step-by-step explanation:
[tex]P(0)=0.023(0)^3-0.289(0)^2+3.068(0)+55.170=55.17[/tex]
A pole that is 3.1 m tall casts a shadow that is 1.46 m long. At the same time, a nearby tower casts a shadow that is 38.5your answer to the nearest meter.long. How tall is the tower RoundIM
82 meters
Explanation
Step 1
Draw:
as the angle of the sun´s ligth is the same for both, we have two congruent trianges, then we can make a proportion
[tex]\text{ratio}=\frac{heigth}{\text{shadow}}[/tex]so
[tex]\begin{gathered} \text{ratio}_1=ratio2 \\ \text{replacing} \\ \frac{3.1}{1.46}=\frac{x}{38.5} \\ to\text{ solve, multiply both sides by 38.5} \\ \frac{3.1}{1.46}\cdot38.5=\frac{x}{38.5}\cdot38.5 \\ 81.74\text{ m=x} \\ \text{rounded} \\ x=82 \end{gathered}[/tex]therefore, the heigth of the tower is
82 meters
Find the exact value of the indicated trigonometric function of θ.
cos θ = (2/5), tan θ < 0 Find sin θ.
The exact value of indicated trigonometric function, sin θ is -0.92
How to find a sine relation when a cosine relation is given?The sine relation is the ratio of the height to the hypotenuse. Meanwhile, the cosine relation is the ratio of the base to the hypotenuse.
The relation of sine and cosine is given as follows:
[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}[/tex]
It is given that cos θ = (2/5)
So, the sine value can be obtained from the given value.
[tex]\sin \theta=\pm\sqrt{1-\cos^2\theta}\\=\pm\sqrt{1-(2/5)^2}\\=\pm\sqrt{21}/5\\ =-0.92[/tex]
So, the sine value for the given cosine value is - [tex]\sqrt{21}/5[/tex] or -0.92.
Note that we omitted the positive value because it is given that the tangent value is negative, so the angle lies in the fourth quadrant, where the sine value is also negative.
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Find the intercepts (if an answer does not exist enter DNE) be sure to graph the line as well
Question:
Solution:
x-intercept:
the x-intercept is when y= 0. Thus replacing this value into the given equation we get:
[tex]15x+10(0)\text{ = 30}[/tex]this is equivalent to:
[tex]15x+0\text{= 30}[/tex]this is equivalent to:
[tex]15x\text{ = 30}[/tex]solving for x, we get:
[tex]x\text{ = }\frac{30}{15}\text{ = 2}[/tex]so the point of x-interception is :
[tex](x,y)\text{ = (2,0)}[/tex]y-intercept:
the y-intercept is when x= 0. Thus replacing this value into the given equation we get:
[tex]15(0)+10y=30[/tex]this is equivalent to:
[tex]0\text{ + 10y = 30}[/tex]this is equivalent to:
[tex]10y\text{ = 30}[/tex]solving for y, we get:
[tex]y\text{ = }\frac{30}{10}=\text{ 3}[/tex]so the point of y-interception is :
[tex](x,y)\text{ = (0,3)}[/tex]We can conclude that the correct answer is:
x-intercept :
[tex](x,y)\text{ = (2,0)}[/tex]y-intercept is :
[tex](x,y)\text{ = (0,3)}[/tex](d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
A school is installing a flagpole in the central plaza. The plaza is a square with side length 100 yards as shown in the figure below. The flagpole will take up a square plot in the middle of the plaza and its base will have an area of x2−10x+25 yd2. Area of the flagpole plot: x2−10x+25 A plaza square with a small flagpole square in the middle. 100 yards100 yards Find the length of the base of the flagpole by factoring. (Hint: Because the area of the flagpole is an expression that involves the variable x, the length of the base will also involve the variable x.) The length of the base of the flagpole is
The area of the flagpole is:
[tex]x^2-10x+25[/tex]This represents a perfect square, because it can be represented as below:
[tex]x^2-2\cdot5+5^2[/tex]Therefore we can use the notable product, square of the difference to factor the expression:
[tex](x-5)^2=(x-5)\cdot(x-5)[/tex]Since the area of the flagpole is the product between it's length and width, then we know that the length and width are equal and are equivalent to:
[tex]\text{length}=\text{width}=(x-5)[/tex]Are the following ratios equivalent?5cookies:9 glasses of milk and 3 cookies :12 glasses of milk
Answer:
No
Step-by-step explanation:
5:9 and 3:12 do not divide with the same number
For example:
3:6 and 9:18 would be equivalent as dividing 9:18 by 3 would give 3:6
Express 55 miles per hour in kilometers per hour.km/hr(Round to the nearest whole number as needed.)
Okay, here we have this:
Considering the provided amount in miles per hour, we are going to convert it to kilometers per hour, so we obtain the following:
[tex]\begin{gathered} \frac{55mi}{h}\cdot\frac{1.6km}{1mi} \\ =\frac{55\cdot1.6km}{h} \\ =88\frac{\text{ mi}}{h} \end{gathered}[/tex]Finally we obtain that 55 miles per hour are equivalent to 88 kilometers per hour.
Write the exponential function y - 45(1.085)^t in the form y = ae^kt(a) Once you have rewritten the tormula, give & accurate to at least four decimal places.K=If T is measured in years, indicate whether the exponential function is growing or decaying and find he annual and continuous growth/decay rates. The rates you determine should be positive in the case of growth or decay (by choosing decay the negative rate is implied).(b) The annual (growth/decay) rate is ___ % per yearC) The continuous (growth/decay) rate is ___ % per year
EXPLANATION
Given the exponential function:
45(1.085)^t
We have that 45=a is the initial value and 1.085 is the growth rate,
1.085 - 1 = 0.085* 100 = 8.5 % (This is the growth rate)
Let's compute the function with two values of t, as for instance, t=0 and t=1:
[tex]f(0)=45(1.085)^0=45\cdot1=45\longrightarrow\text{ (0,45)}[/tex][tex]f(1)=45\cdot(1.085)^1=48.825\text{ }\longrightarrow\text{(1,48.825)}[/tex]Now, the function in the form y = ae^kt will be as follows:
[tex]y=45\cdot e^{kt}[/tex]Substituting t by 1:
[tex]y(1)=45\cdot e^k=48.825[/tex]Dividing both sides by 45:
[tex]e^k=\frac{48.825}{45}=1.085[/tex]Applying ln to both sides:
[tex]k=\ln 1.085[/tex]Computing the argument:
[tex]k=0.0816[/tex]The expression will be as follows:
[tex](a)---\longrightarrow y=45e^{0.0816t}[/tex]As this is a growing function, the rates are positive.
The annual growth rate is 8.5% and It's was calculated above.
Now, we need to compute the continuous rate because It's given by the value of k:
k = 0.0816 --> Multiplying by 100 --> 0.0816 * 100 = 8.16%
The continuous growth rate is 8.16%
Which situation yields data with variability?The distance covered by different vehicles traveling at a constant rate of 60 mph for 45 minutes The length of different professional American football fieldsThe weight of 6th grade studentsThe moon cycle duration in a year
Answer:
The weight of 6th-grade students
Explanation:
We have variability if each value in the data is different.
When a vehicle travels at a constant rate for the same amount of time, the distance covered will be always the same. So, this situation doesn't yield data with variability.
In the same way, the length of a professional American football field and the moon cycle duration in a year are standard, they always have the same value so these situations don't yield data with variability.
Finally, each student of 6th grade has a different weight, so this is the situation that yields data with variability.
Therefore, the answer is:
The weight of 6th-grade students
What’s the correct answer answer asap for brainlist
Answer:
B
Step-by-step explanation:
Answer: B. Symbolic - the "Queen" represents suppression and deceit.
Which term describes the slope of the line below?
•
A. Undefined
B. Zero
• C. Positive
D. Negative
Answer:
D. Negative
Step-by-step explanation:
The slope is negative because the line goes down from left to right. In other words, as x increases, y decreases.
A slope would be positive when the line goes up from left to right. In other words, as x increases, y increases.
A slope would be zero if the line is horizontal, so as x increases, y remains constant.
A slope would be undefined if the line is vertical. It is undefined because x remains constant while y changes. Lines are functions, which mean for every input there is exactly 1 output. If there are multiple y values for 1 x value, then this is not a function and therefore has an undefined slope.
3. How many tens are there between 9,312 and 9,522? Explain your thinking
The number of tens between the given numbers are 1883.
The number of tens between two numbers can be calculated by the concept of proportions. A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem. Now, to find the number of tens we divide the number by 10. So, the number of tens in the given numbers are
9312/10 = 931 (approximately)
9522/10 = 952 (approximately).
Now, the numbers of tens between the two given numbers can be calculated by adding the number of tens in them that is,
952 + 931 = 1883 tens between the two numbers.
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Write in terms of the cofunction of a complementary angle.
given the expression
[tex]sin(\frac{\pi}{15})[/tex]since
[tex]sin(\theta)=\frac{1}{csc(\theta)}=cos(\frac{\pi}{2}-\theta)[/tex]then
[tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{\pi}{2}-\frac{\pi}{15})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=\frac{1}{csc(\frac{\pi}{15})}=cos(\frac{(15-2\pi)}{30})[/tex][tex]s\imaginaryI n(\frac{\pi}{15})=cos(\frac{13\pi}{30})[/tex]ten the correct answer is
Option C
How do I solve for the role of 0 in this equation?(x²-9)(x³-8)=0
Given the equation
[tex](x^2-9)\cdot(x^3-8)=0[/tex]you should have in mind that the expression x^2-9 and x^3-8 are "numbers" and that the product of two numbers is zero if and only if one of the numbers is zero. Then, by using this, you get the following auxiliary equations
[tex]x^2-9=0[/tex]which is equivalent to
[tex]x=\sqrt[]{9}[/tex]so x=3 o x=-3.
Finally, for the other case
[tex]x^3-8=0[/tex]So
[tex]x=\sqrt[3]{8}=2[/tex]so the three possible solutions for the equation are x=3, x=-3 and x=2
1 5/6+1 3/6 pls help
Answer:
10/3
Step-by-step explanation:
[tex]1\frac{5}{6} = \frac{11}{6}\\ \\\ 1\frac{3}{6} = \frac{9}{6}[/tex]
11/6 + 9/6 = 10/3 =3.333333333
Which expression is missing from step 7?
OA.(d- e)²
OB. -2de
OC. (A+B)2
OD. A²+ B²
The correct option A. (d- e)², is the expression is missing from step 7.
What is termed as the Pythagorean theorem?The Pythagorean theorem, or Pythagorean theorem, tries to explain the relationship among the three sides of such a right-angled triangle. The square on the hypotenuse is equal to the total of the squares of the remaining two sides of a triangle, according to Pythagoras' theorem. According to Pythagoras' theorem, when a triangle has been right-angled (90 degrees), the square of the hypotenuse equals the sum of the squares of the remaining two sides.For the given question.
The missing value of the 7th term is -
(√1 + d²)² + (√e² + 1)² = (d- e)²
Such that the 8th terms becomes after squaring the both sides are;
(1 + d²) + (e² + 1) = d² + e² - 2de.
Thus, the missing term in the step 7 is (d- e)².
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(a) Give a secant line.(b) Give a chord.(c) Give a tangent line.
Solution
Secant is a line that touches a circle at two distinct points
See figure below
Chord is a straight line that touches two points on the the circumference of the circle
A
The variable cost for a product is $1.00 and the total fixed costs are $88,000. The company sells the products for $3.00 each. How many products will the company have to sell to break even?
The breakevenpoint is the point at which costs and sales are equal to each other and therefore, the profit is zero.
The breakeven point in terms of number of units sold can be determined as follows;
[tex]\begin{gathered} Breakeven\text{ units=}\frac{Fixed\text{ costs}}{\text{ Selling price per unit-}Variable\text{ cost per unit}} \\ \text{Breakeven units=}\frac{88000}{3-1} \\ \text{Breakeven units=}\frac{88000}{2} \\ \text{Breakeven units=44000} \end{gathered}[/tex]In order to breakeven, the company will have to sell 44,000 units
Please Answer the following 2 questions asked in the image provided, Asap.
1 Fristly you do M1=M2 as it is parallel
You get M2 then use it to find equation
note that y= -1.5
2 for second question you find coefficient of X and y you get M1 then find equation of given line easily.
#note equaction of straight line passing through two points is y-y1=m(x-x1)
For each relation, decide whether or not it is a function.
Relation 1: No, the inputs of desk and leaf each correspond to two different outputs.
Relation 2: No, the input of 7 corresponds to three different outputs.
Relation 3: Yes, each input corresponds to only one output.
Relation 4: No, the input of -7 corresponds to two different outputs: a and h.
In the figure above, if k II I, what is the value of y?
B. 45
C. 50
A. 40
D. 60
The values of measure of angle y is found as 65 degrees.
What is defined as the linear pair?Once two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to one another after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair has always been 180°. These angles are also referred to as supplementary angles. A adjacent angles are those that share a vertex. As a result, the linear angles get a common vertex here as well.For the given question;
Line k || Line l
(x + 5) + (3x + 15) = 180 (linear pair)
Solving;
4x + 20 = 180
4x = 160
x = 40
Put the value of x in angles (2x + 30)
2x + 30 = 2×40 + 30 = 110
Now,
2x + 30 = y + (x + 5) (alternate interior angles)
Solving;
110 = y + 40 + 5
y = 110 - 45
y = 65 degrees.
Thus, the values of measure of angle y is found as 65 degrees.
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