One tablet contains 150 mg of the active ingredient. Then, 90 tablets contain
[tex]90\text{ tablets }\cdot\frac{150\text{ mg}}{1\text{ tablet}}=13500mg_{}[/tex]1 gram is equivalent to 1,000 mg, then 13500 mg is equivalent to
[tex]13500\text{ mg}\cdot\frac{1\text{ gram}}{1000\text{ mg}}=13.5\text{ grams}[/tex]There are 13.5 grams of the active ingredient in the entire bottle
43 pointThe length of a rectangular box is 5 inches longer than twice the width (x).The height is 6 inches.Which is the volume (y) when the width (x) is 9 inches
L = 2*9+5=23
Find the direction angle of vector v to the nearest tenth of a degree.Equation editor does not include the grouping symbols "<" and ">" that are necessary for writing avector in component form. For this question, use braces to write a vector in component form. Forexample, the vector < 2,3> should be written as {2,3}.
The direction angle is approximately 9.5 degrees
Explanation:The vectors are {-5, 0} and {7, 2}
Direction vector is {7 - (-5), 2 - 0 } = {12, 2}
Direction angle is:
[tex]\tan^{-1}(\frac{2}{12})\approx9.5^o[/tex]The points represented by the table lie on a line. How can you find the slope of the line from the table? What is the slope of the line? Х 2 4 6 8 y 5 1 -3 -7
The given table is
x 2 4 6 8
y 5 1 -3 -7
The formula for determining the slope of a line is expressed as
slope = (y2 - y1)/(x2 - x1)
From the table,
x1 = 2, x2 = 4
y1 = 5, y2 = 1
Slope = (1 - 5)/(4 - 2)
Slope = - 4/2
Slope = - 2
A meteorologist collected data about wind speed in a city, in miles per hour, on consecutive days of a month. Her data is shown using the dot plot. Create a box plot to represent the data. (1 point)
dot plot titled Monthly Wind Speed and number line from 9 to 10 in increments of 1 tenth labeled Wind Speed (in miles per hour) with zero dots over 9, 1 dot over 9 and 1 tenth, 2 dots over 9 and 2 tenths, 1 dot over 9 and 3 tenths, 3 dots over 9 and 4 tenths, zero dots over 9 and 5 tenths, 1 dot over 9 and 6 tenths, 2 dots over 9 and 7 tenths, 1 dot over 9 and 8 tenths, zero dots over 9 and 9 tenths, and zero dots over
box plot with minimum value 9 and 2 tenths, lower quartile 9 and 3 tenths, median 9 and 5 tenths, upper quartile 9 and 8 tenths, and maximum value 9 and 9 tenths
box plot with minimum value 9 and 1 tenth, lower quartile 9 and 2 tenths, median 9 and 4 tenths, upper quartile 9 and 7 tenths, and maximum value 9 and 8 tenths
box plot with minimum value 9 and 1 tenth, lower quartile 9 and 3 tenths, median 9 and 4 tenths, upper quartile 9 and 6 tenths, and maximum value 9 and 8 tenths
box plot with minimum value 9 and 1 tenth, lower quartile 9 and 2 tenths, median 9 and 5 tenths, upper quartile 9 and 7 tenths, and maximum value 9 and 8 tenths
The correct box plot to represent the data on wind speed is: minimum at 9.1, first quartile at 9.2, median at 9.4, 3rd quartile at 9.7, maximum at 9.8.
What is a boxplot?
A boxplot refers to a type of chart that can be used to graphically represent and show the five-number summary of a data set with respect to locality, skewness, and spread. Thus, the five-number summary include the following:
Minimum
First quartile
Median
Third quartile
Maximum
Based on the data on wind speed in a city, the minimum should be at 9.1, first quartile at 9.2, median at 9.4, 3rd quartile at 9.7, and maximum at 9.8.
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Answer:
I believe the answer is C.
Step-by-step explanation:
The point starts at 91 then goes up all the way to 94 making that the line thing (I cant remember the terms) then the end of the box would be 97 because you want the line to end at the last dot thats on 98
I hope this isnt confusing thats just how I got C
Please just give me answer checking my answers to make sure my answers ok. I don't need the steps
Given:
The explicit formula for a geometrc sequence is given:
[tex]a_n=500\times(0.5)^{n-1}[/tex]To find the 6th term put n=6 here,
[tex]\begin{gathered} a_6=500\times(0.5)^{6-1} \\ =500\times(0.5)^5 \\ =500\times0.03125 \\ =15.625 \end{gathered}[/tex]Hence, option B is correct.
I need help to do these composition of functions. I have a photo if needed.g(a)=a-1f(a)=3a-1Find (g×f)(1)
According to the definition for composite function,
[tex]g\circ f(x)=g\lbrack f(x)\rbrack[/tex]Substitute the values,
[tex]\begin{gathered} g\circ f(1)=g\lbrack f(1)\rbrack \\ g\circ f(1)=g\lbrack3(1)-1\rbrack \\ g\circ f(1)=g\lbrack2\rbrack \\ g\circ f(1)=(2)-1 \\ g\circ f(1)=1 \end{gathered}[/tex]Thus, the value of the given composite function is 1.
identify the table that would correctly graph the equation y=3x
To be able to determine which table would correctly graph the equation y = 3x, let's one pair of data in the table and substitute it to the equation. The data that satisfies the equation is therefore the one that would correctly graph the equation.
We get,
A.) x = 0 and y = 2
y = 3x
2 = 3(0)
2 = 0
Therefore, this table will not correctly graph the equation.
B.) x = 0 and y = 4
y = 3x
4 = 3(0)
4 = 0
Therefore, this table will not correctly graph the equation.
C.) x = 0 and y = 1
y = 3x
1 = 3(0)
1 = 0
Therefore, this table will not correctly graph the equation.
D.) x = 0 and y = 0
y = 3x
0 = 3(0)
0 = 0
Therefore, this table will correctly graph the equation.
The answer is letter D.
findind percent proportions
Thus, the boys percantage is 45%.
Clean Machine is Middletown's premier house cleaning service. The company used 2,920 gallons of soap last year, and 35% less this year. How many gallons of soap did the company use this year?
Answer:
Step-by-step explanation:)
Solve the given equation over the interval [0, 2.2): 2 cos2 x + cos x + 15 = 0.X = 0 and x = 2.0T57x= - and x=66There are no real valued solutions for the equation.T371x= and x =2
The given function is
[tex]2\cos ^2x+\cos x+15=0[/tex]Solve the equation to get:
[tex]\cos x=\frac{-1\pm\sqrt[]{1-4\ast2\ast15}}{4}=\frac{-1\pm\sqrt[]{-119}}{4}[/tex]The square root of a negative number is not real hence there are no real valued solutions
Option C is correct.
Last month the mail carrier delivered mail on the morning route 16 times and on the afternoon route 12 times for a total distance of 141 miles. This month the mail carrier delivered mail on the morning route 10 times and on the afternoon route 15 times, for a total distance traveled of 123.75 miles. What is the distance of the morning route in miles?
The distance of the morning route is 5.25 miles.
What is the distance of the morning route?The first step is to form a system of equations that would represent the information in the question:
16m + 12a = 141 equation 1
10m + 15a = 123.75 equation 2
The equations would be solved using the elimination method:
Multiply equation 1 by 5 and equation 2 by 4
80m + 60a = 705 equation 3
40m + 60a = 495 equation 4
Subtract equation 4 from equation 3:
40m = 210
Divide both sides of the equation by 40
m = 210 / 40
m = 5.25 miles
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4. Find the equationof a line with a slopeof 3 and through(2,9)
to find the equation we need to use the slope-point equation, and we get the following
[tex]\begin{gathered} y-9=3(x-2)=3x-6 \\ y=3x-6+9=3x+3 \end{gathered}[/tex]so the answer is
[tex]y=3x+3[/tex]HELP ASAP!!!
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.
A mapping diagram with one circle labeled x-values containing values negative 4, negative 2, 0, 1, and 3 and another circle labeled y values containing values negative 5, negative 4, negative 3, negative 2, and negative 1 and arrows from negative 4 to negative 5, negative 2 to negative 3, 0 to negative 4, 0 to negative 2, 1 to negative 3, and 3 to negative 1.
Is the relation a function? Explain.
No, because for each input there is not exactly one output
No, because for each output there is not exactly one input
Yes, because for each input there is exactly one output
Yes, because for each output there is exactly one input
Answer:
This relation is not a function. For each input, there is not exactly one output.
The relationship in the given diagram is not a function, because for each input there is not exactly one output. So Option A is correct
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
Values of x and values of y
In given diagram,
for x = 0,
there are two values of y, -4 and -2
but according to definition of y, it should give only one value
Hence, it is not a function
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Which picture below represents ?
5 2
10
Pls help
Answer:
b
Step-by-step explanation:
ABC reflected across the x-axis and then dilated by a factor of 12
Solution:
Given the figure;
The reflection rule across the x-axis is;
[tex]P(x,y)\rightarrow P^{\prime}(x,-y)[/tex]Thus, the point A(3,1) after reflection is;
[tex]A(3,1)\rightarrow A^{\prime}(3,-1)[/tex]Then, dilated by a factor of 2 using the point (-2,1) as the center of dilation.
Thus;
[tex]\begin{gathered} A^{\prime}(3,-1) \\ (-2,1) \\ \\ A^{\prime}(5,-2) \\ \\ A^{\prime}(5,-2)\rightarrow2(5,-2)\rightarrow(10,-4) \\ \\ A^“(10,-4) \\ (-2,1) \\ \\ A^“(8,-3) \\ \\ \end{gathered}[/tex]CORRECT OPTION: (B) A"(8,-3)
A recipe for flour requires 2 cups of flour, 1 cup of shortening, and 1 cup of milk and makes 1 dozen biscuits. how many biscuits can you make of you triple the recipe?
The given recipe for 1 dozen biscuits is
• 2 cups of flour.
,• 1 cup of shortening.
,• 1 cup of milk.
Now, we have to multiply each number by 3 in order to triple the recipe. So, the recipe for 3 dozens is
• 6 cups of flour.
,• 3 cups of shortening.
,• 3 cups of milk.
Hence, the total number of biscuits obtained from the new recipe is 36, which is equivalent to 3 dozens.Dennis invest $4000 into an account that pays at a 3.5% interest rate compounded continuously. How many years will it take until Dennis has $6000 in his account? Round your answer to the nearest year 
Answer:
12 years
Explanation:
For an investment whose interest is compounded continuously, the amount in the account after t years is determined using the formula:
[tex]A(t)=P_oe^{rt}\text{ where }\begin{cases}{P_o=\text{ The amount invested}} \\ r=Interest\text{ }{Rate} \\ {t}=Time\end{cases}[/tex]In our given problem:
• A(t) = $6,000
,• Po = $4000
,• r = 3.5% = 0.035
We want to find the value of t.
Substitute the given values into the formula:
[tex]6000=4000e^{0.035t}[/tex]Then solve for t:
[tex]\begin{gathered} \text{ Divide both sides by 4000} \\ \frac{6000}{4000}=\frac{4000e^{0.035t}}{4000} \\ 1.5=e^{0.035t} \\ \text{ Take the ln of both sides:} \\ \ln(1.5)=\ln(e^{0.035t}) \\ 0.035t=\ln(1.5) \\ \text{ Divide both sides by }0.035 \\ \frac{0.035t}{0.035}=\frac{\operatorname{\ln}(1.5)}{0.035} \\ t=11.58 \\ t\approx12\text{ years} \end{gathered}[/tex]It will take Dennis 12 years (rounded to the nearest year) before he has $6,000 in his account.
Identify relative maximum and the relative minimum points on the graph, if any y=x^3-2x^2-3x
The relative maximum on the graph is approximately
The relative minimum on the graph is approximately
STEP - BY - STEP EXPLANATION
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 26 ft long and 18 ft wide.
Find the area of the garden. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the rose garden formed by joining a rectangle and a semicircle is 595.17 ft².
How to find the area of a composite figure?The rose garden is formed by joining a rectangle and a semicircle. The rectangle is 26 ft long and 18 ft wide.
The area of the garden can be found as follows:
area of the garden = area of the rectangle + area of the semi circle
Therefore
area of the garden = lw + 1 / 2πr²
l = 26 ft
w = 18 ft
r = 18 / 2 = 9 ft
area of the garden = 26 × 18 + 1 / 2 × 3.14 × 9²
area of the garden = 468 + 254.34 / 2
area of the garden = 468 + 127.17
area of the garden = 595.17 ft²
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write the equation of a circle given the center (-4, 4) and radius r = 5
Given : the center of the circle = (-4 , 4)
And the radius of the circle = r = 5
The general equation of the circle is :
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) is the center of the circle and r is the radius of the circle
So, ( h , k ) = ( -4 , 4 ) and r = 5
so, the equation of the circle will be :
[tex]\begin{gathered} (x-(-4))^2+(y-4)^2=5^2 \\ \\ (x+4)^2+(y-4)^2=25 \end{gathered}[/tex]1,000,000 × 100can u help me
15 1/3 ÷ 3 5/6 A. 45 6/9 B. 5 1/4 c . 4 d. 4 1/3
To compute 15 1/3 ÷ 3 5/6, first transform the mixed numbers into fractions, as follows:
[tex]15\frac{1}{3}=\frac{15\cdot3+1}{3}=\frac{46}{3}[/tex][tex]3\frac{5}{6}=\frac{3\cdot6+5}{6}=\frac{23}{6}[/tex]Then, 15 1/3 ÷ 3 5/6 = 46/3 ÷ 23/6. Dividing by a fraction is equivalent to multiply by its inverse, then 46/3 ÷ 23/6 = 46/3 x 6/23:
[tex]\frac{46}{3}\cdot\frac{6}{23}=\frac{46}{23}\cdot\frac{6}{3}=2\cdot2=4[/tex]In a city 20% of the cars are electric, 16% of the cars are red, and 14% of the cars are red electriccars. If a car is randomly picked and found to be red, what is the probability that this car is electric?Enter your answer as a decimal number rounded to TWO digits after the decimal point, like 0.12.DO NOT enter it like 12% or 12.
Pls help: find the rational expression state any restrictions on the variable
Simplification of Rational Expressions
Given the rational expression:
[tex]\frac{n^4-10n^2+24}{n^4-9n^2+18}[/tex]Simplify and state the restriction for the variable n.
Let's work on the numerator and denominator independently. Factoring the numerator:
[tex]\begin{gathered} n^4-10n^2+24=n^4-4n^2-6n^2+24 \\ n^4-10n^2+24=n^2(n^2-4)-6(n^2-4) \\ n^4-10n^2+24=(n^2-6)\mleft(n^2-4\mright) \end{gathered}[/tex]The denominator can be factored in a similar way:
[tex]\begin{gathered} n^4-9n^2+18=n^4-3n^2-6n^2+18 \\ n^4-9n^2+18=n^2(n^2-3)-6(n^2-3) \\ n^4-9n^2+18=\mleft(n^2-3\mright)(n^2-6) \end{gathered}[/tex]Thus, rewriting the expression:
[tex]\frac{n^4-10n^2+24}{n^4-9n^2+18}=\frac{(n^2-4)(n^2-6)}{(n^2-3)(n^2-6)}[/tex]Before simplifying, we must state the restrictions for the variable. The denominator cannot be 0, thus:
[tex]\begin{gathered} n^2-3\ne0\Rightarrow n\ne\pm\sqrt[]{3} \\ n^2-6\ne0\Rightarrow n\ne\pm\sqrt[]{6} \end{gathered}[/tex]Now simplify:
[tex]\frac{n^4-10n^2+24}{n^4-9n^2+18}=\frac{(n^2-4)}{(n^2-3)}[/tex]Combining the final expression with the restrictions, we stick with choice a.
If you solved the following system by substitution, which of these could be yourcombined equation?y = 3x - 44x + 3y = 1
To solve the given system, we have to combine the equations
[tex]\begin{gathered} 4x+3y=1 \\ 4x+3(3x-4)=1 \\ 4x+9x-12=1 \\ 13x=12+1 \\ 13x=13 \\ x=\frac{13}{13} \\ x=1 \end{gathered}[/tex]Then, we find y
[tex]y=3x-4=3\cdot1-4=3-4=-1[/tex]Hence, the solutions (1,-1,). C is the answer.5. Given: Line segment AD bisects
Given information:
AD bisects
We are in a triangle that has been bisected , and therefore, the segment AD cuts the side BC of the triangle in two equal parts.
Also, since AD bisects the angle, <1 equals <2.
Step 1: Angle bisector defines two equal angles, then <1 = <2
They also tell us that angle <3 = <1 (premise)
Then, using transitive property we have:
<1 = <3
and <1 = <2 due to result of a bisection
then using transitive property:
<3 = <1 = <2
<3 = <2
Just lmake sure you use "transitive" property as the reason for the congruency in the last step.
Researchers are studying the relationship between dog ownership and depression. A large group of people were surveyed, and the data is summarized in the table below. What is the odds ratio of not being depressed for those who have a dog?
Depressed Not Depressed Total
Owns a Dog 251 412 663
Does Not Own a Dog 374 305 605
Total 625 717 1,342
Round your answer to the hundredths place.
Provide your answer below:
Answer: 2.01
Step-by-step explanation
“Odds of a person who owns a dog is NOT depressed”/ “odds of a person who does NOT own a dog is NOT depressed”
aka
(412/251)/(305/374) =
412/251 x 374/305=
154,088/77,555…
total answer= 2.01
The odds ratio of not being depressed for those who have a dog
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
It is given that, The data is,
Depressed Not depressed Total
Owns a dog 251 412 663
Does not owns a dog 625 717 1342
The probability that a dog owner is not depressed is equivalent to the likelihood that a dog owner is not depressed.
Thus, the odds ratio of not being depressed for those who have a dog
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15
Be sure to read the directions carefully and write what is asked for.
Part A: Multiply (without simplifying your answer): 5√12 2√/6 =
Part B: What perfect square can you take out of the radicand from Part A's answer?
Part C: After simplifying, what is the final answer to Part A?
The product of radical numbers is 10√72. The simplest form of the radical part is 60√2.
What is the meaning of radical?
The square root or nth root is represented by the symbol √. Expression with a square root is referred to as a radical expression. Radicand: A value or phrase included within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
Given numbers are 5√12 and 2√6.
Now multiply the given numbers:
5√12 × 2√12
Multiply whole number with whole number and radical part with radical part:
=(5 × 2) × (√12 ×√6)
= 10 × √72
= 10√72
= 10 √(6 × 6 × 2)
Take out perfect square of the radicand:
= 10 × 6 √( 2)
= 60√2
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The perimeter of rectangle A is 10 cm and its area is 6 cm2. The perimeter of rectangle B is 20 cm. What is the area of rectangle B assuming these two rectangles are similar?
The perimeter of rectangle A is 10 cm
Perimeter of A = 2x+2y=10 cm, then:
Perimeter of A = 2(x+y)=10
Perimeter of A = x+y=5
We also know that the area of A= xy= 6 cm²
Then, we can admit x=3 and y=2.
Both rectangles are similar.
[tex]\frac{x_a}{y_a_{}}=\frac{x_b}{y_b}[/tex][tex]\begin{gathered} \frac{3}{2}=\frac{x_b}{y_b} \\ x_b=\frac{3y_b}{2_{}} \end{gathered}[/tex]Perimeter of B
[tex]\begin{gathered} 2x_b+2y_b=20 \\ x_b+y_b=10 \\ \frac{3y_b}{2}+y_b=10 \\ 3y_b+2y_b=20 \\ 5y_b=20 \\ y_b=4 \end{gathered}[/tex][tex]\begin{gathered} x_b=\frac{3y_b}{2} \\ x_b=\frac{3\cdot4}{2} \\ x_b=\frac{12}{2} \\ x_b=6 \end{gathered}[/tex]Therefore
Area of B = 4 x 6 cm² = 24 cm²
In ABCD, the measure of ZD=90°, CB = 53, BD = 45, and DC = 28. What ratiorepresents the sine of ZB?|
SOLUTION
Step 1 :
In this question, we asked to find the value of
[tex]\sin \text{ B}[/tex][tex]\begin{gathered} \text{where }\angle D=90^0 \\ BD\text{ = 45} \\ DC\text{ = 28} \\ BC\text{ = 53} \end{gathered}[/tex]Step 2 :
We can are see clearly that 28 , 45, 53 ) iPythagoras' Triple, since:
[tex]28^2+45^2=53^2[/tex]Step 3 :
[tex]\begin{gathered} \sin \text{ B = }\frac{28}{53} \\ =\text{ 0.5283} \end{gathered}[/tex]CONCLUSION :
[tex]\sin \text{ B = 0.5283}[/tex]