Answers
The magnitude of a number is the absoulute value of the number. Recall, the absolute value of a number is always positive. The absolute value of a is written as IaI
Hence,
magnitude of - 7.5 is 7.5
The correct option is D
Related Questions
PLEASE HELP I’M IN MIDDLE SCHOOL AND I CANT FIND THE ANSWERS. ITS ALSO DUE IN A FEW HOURS.
Answers
To form a triangle the three angles must follow the inequality principle that says: The sum of any two sides must always be greater than the length of the third side. With this in mind let's check the angles.
For the first item we have:
[tex]\begin{gathered} 70+90>20\rightarrow160>20 \\ 70+20>90\rightarrow90>90 \\ 20+90>70\rightarrow110>90 \end{gathered}[/tex]Since the second inequality is invalid the angles don't form a triangle.
For the second item we have:
[tex]\begin{gathered} 55+45>75\rightarrow100>75 \\ 55+75>45\rightarrow130>45 \\ 45+75>55\rightarrow120>55 \end{gathered}[/tex]Since all the inequations are valid then the angles form a triangle. Since all the angles are smaller than 90 degrees, then this is an acute triangle.
For the third item we have:
[tex]\begin{gathered} 27+27>126\rightarrow54>126 \\ 27+126>27\rightarrow153>27 \end{gathered}[/tex]Since the second inequation is invalid, then the angles don't form a triangle.
For the fourth item we have:
[tex]\begin{gathered} 38+87>55\rightarrow125>55 \\ 38+55>87\rightarrow93>87 \\ 55+87>38\rightarrow142>38 \end{gathered}[/tex]Since all the inequalities are valid, then the angles form a triangle. All of its angles are smaller than 90 degrees, therefore this triangle is an acute triangle.
A rectangular yard is 22 ft by 19 ft. The yard is covered with grass except for a square flower garden 10.5 ft long. How much grass is in the yard? The area covered by grass is (Type a whole number or a decimal.)
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A rectangular yard is 22 ft by 19 ft. The yard is covered with grass except for a square flower garden 10.5 ft long. How much grass is in the yard? The area covered by grass is (Type a whole number or a decimal.)
we have that
The area covered by grass is equal to the area of a rectangular yard minus the area of the square flower garden
so
A=(22)(19)-(10.5)^2
A=307.75 ft2Which of the following is graphed below?
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The function that is graphed here is option A;
y = {x³ - 3, x ≤ 2 and x² + 6, x > 2
Given,
The graph
Function;
A function is a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).
We have to find the function that is graphed here from the given options.
Here,
The function that is graphed here is option A;
y = {x³ - 3, x ≤ 2 and x² + 6, x > 2
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is a projectile is launched from a height of 5 m with an intial velocity of 25 meters per second, how many seconds will it take the projectile to hit the ground
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In this problem we know that the initial velocity in the horizontal axis is 25, however the initial velocity in the y axis will be o so we can use this equation:
[tex]y=y_0+v_it+\frac{1}{2}at^2[/tex]So to find the time the object get the grownd we can replace the initial high for 5 miter, the final one for 0 and the aceleration by -9.8 (gravity) so:
[tex]0=5+0(t)+\frac{1}{2}(-9.8)t^2[/tex]and we solve for t so:
[tex]\begin{gathered} 9.8t^2=5\cdot2 \\ t^2=\frac{10}{9.8} \\ t\approx\sqrt[]{1} \\ t\approx1 \end{gathered}[/tex]So the projectil takes one secon to hit the grownd
The table below represents the data collected at a sandwich shop for the last six months withrespect to the type of bread people ordered (sourdough or wheat) and whether or not theygot cheese on their sandwich.With cheeseWithout cheeseSourdough800425Wheat1200700What is the P(cheese | wheat)? Show all work to receive full credit. You can place your workin this box or attach it in the box on the final question.
Answers
Given:
The table represents the data collected at a sandwich shop for the last six months with respect to the type of bread
We will find P(cheese | wheat)
We will use the following formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Let A represents cheese, and B represents wheat
From the table:
[tex]\begin{gathered} A\cap B=1200 \\ B=1200+700=1900 \end{gathered}[/tex]So, the probability will be as follows;
[tex]P\left(cheese|wheat\right)=\frac{1200}{1900}=\frac{12}{19}[/tex]So, the answer will be:
P(cheese | wheat) = 12/19 = 0.63
Simply the expression. (Cos x) (sec x)-(sin^2 x)
Answers
[tex]Cos^{2}x[/tex] is the solution for the expression [tex](Cosx)(secx) - sin^{2}x[/tex]
The given expression is:
[tex](Cosx)(secx) - sin^{2}x[/tex]
Recall form Pythagorean Identity that;
[tex]secx = \frac{1}{cosx}[/tex]
We apply this property to obtain;
[tex](cosx)(\frac{1}{cosx}) - sin^{2}x[/tex]
By simplifying we get that;
[tex]1 - sin^{2}x[/tex]
Recall from the Pythagorean, we identity that;
[tex]1 - sin^{2}x = cos^{2}x[/tex]
Hence the answer is [tex]cos^{2}x[/tex] is the solution for the expression [tex](Cosx)(secx) - sin^{2}x[/tex]
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Transformation (x + 2, y - 3) is applied to triangle ABC.What are the coordinates of B’ (the transformation of point B)?A) (-5, 3)B) (2, - 1)C) (0, - 2)D) (2, - 3)
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Transformation:
[tex](x+2,y-3)[/tex]The coordinate of B in (x, y) we can get from the graph, which is (-2, 1):
Thus, the transformation based on the information given is:
[tex](-2+2,1-3)[/tex]Simplifying:
[tex](0,-2)[/tex]Answer: C) (0, -2)
A direct variation includes the points (3, 12) and (n, 8). Find n.
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For a direct variation between each point (x, y),
[tex]\begin{gathered} x\propto y \\ x=ky \\ k=\frac{x}{y} \end{gathered}[/tex]For (x₁, y₁) = (3, 12),
[tex]\begin{gathered} k=\frac{3}{12} \\ k=0.25 \end{gathered}[/tex]To find n, consider (n, 8) = (x, y)
[tex]\begin{gathered} x=ky \\ \end{gathered}[/tex]Substituting,
[tex]\begin{gathered} n=0.25\times8 \\ n=2 \end{gathered}[/tex]Therefore, the value of n is 2
Solve this quadratic equation and explains the steps to help you solve it . Also which two specific methods help you to solve it: Is it quadratic formula, Factoring, Square Root Property or Completing square. And explains.
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Recall that the quadratic formula states that, the solutions to the quadratic equation
[tex]ax^2+bx+c=0[/tex]are
[tex]\frac{-b\pm\sqrt{(-b)^2-4ac}}{2a}.[/tex]Now, in the given equation, a=-1 ,b=-6, and c= 8. Therefore, the solutions to the equation are:
[tex]x=\frac{6\pm\sqrt{36+32}}{-2}.[/tex]Simplifying the above result, we get:
[tex]x=-3\pm(-1)\sqrt{17}.[/tex]Answer:
[tex]\begin{gathered} x_1=-3+\sqrt{17,} \\ x_2=-3-\sqrt{17}. \end{gathered}[/tex]Please help with this question: I have attached the image A survey was done where males and females were asked if they would prefer to eat chicken or steak. The results of the survey are shown in the two-way frequency table. ChickenSteakMale0.2380.216Female0.3110.235What percent of the males surveyed prefer chicken?Enter your answer to the nearest tenth of a percent in the box. __%
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23.8%
Explanation:
Since 0.238 represent the frequency of male who eats chicken
0.238 / 100 = 23.8%
Answer: 52.4%
Step-by-step explanation: I took the test and that was the correct answer.
am I supposed to x all this together I need help with the answer please thank you
Answers
The volume of the tank can be calculated using the Volume of a cylinder formula, which is:
[tex]V=\pi\cdot r^2\cdot h[/tex]Where:
v = volume;
r = radius;
h = height.
In this exercise:
r = Diameter/2 = 12/2 = 6 ft
h = 16 ft
So, substituting the values:
[tex]\begin{gathered} V=\pi\cdot6^2\cdot16 \\ V=\pi\cdot36\cdot16 \\ V=576\pi \end{gathered}[/tex]Using π = 3.14:
[tex]\begin{gathered} V=576\cdot3.14 \\ V=1808.64 \\ V=1809ft^3 \end{gathered}[/tex]Answer:
The volume of the tank is 1809 ft³.
Determine the signs of given trigonometric function of an angle in standard position with given measure.cos (-302°) and sin (-302°)
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Exercise: Calculate the sign of cos(-302°) and sin(-302°).
We can know the sign of the trigonometric value of an angle depending on which quadrant the angle is located. In the case of cosine and sine, we have the following rules:
Let's calculate the sign of cos(-302°) first. Note that the angle within the cosine is negative; this means that it must be measured from the x-axis clockwise. Now, every quadrant has a total measure of 90°; then, dividing 302 by 90 we obtain
[tex]\frac{302}{90}\approx3.4,[/tex]which means that -302° goes through two complete quadrants and a partial part of a third one. Since we must measure the angle clockwise, -302 lies in the first quadrant.
By the diagram above, the sign of -302° is +.
On the other hand, looking at the sine diagram, we see that the sign of sine(-302°) is + as well.
AnswerThe signs of cos(-302°) and sin(-302°) are both +.
2. A shop owner raises the price of a $150 pair of shoes by 40%. After a few weeks,because of falling sales, the owner reduces the price of the shoes by 40%. Acustomer then says that the shoes are back at the original price.d. By what percent should the shoes be decreased in order to have the priceback at $150?Kk
Answers
Answer:
Explanations:
Given the following parameters;
Original price of shoe = $150
If the price is increased by 40%, the new price will be expressed as:
[tex]\begin{gathered} New\text{ price}=\$150+(0.40\times\$150) \\ New\text{ price}=\$150+\$60 \\ New\text{ price}=\$210 \end{gathered}[/tex]If the the owner reduces the price of the shoes by 40% due to falling price, hence;
[tex]\begin{gathered} New\text{ price}=210-(0.4\times210) \\ New\text{ price}=210-84 \\ New\text{ price}=\$126 \end{gathered}[/tex]I really need help. volume of this figure using 3.14 without rounding.
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We get that the volume of the figure is the volume for the rectangular prism and the cylinder with radius 4
[tex]\begin{gathered} V=16\cdot11\cdot11+3.14\cdot4^2\cdot9 \\ =1936+452.16 \\ =2388.16 \end{gathered}[/tex]I need help w this question for geometry Find the total area
Answers
Explanation
We are asked to find the total area of the figure
To do so, we will split the area into 2 as shown below
For figure A
We have a trapezoid
The area of a trapezoid is
[tex]\begin{gathered} Area=\frac{1}{2}(a+b)\times height \\ b=13 \\ a=3 \\ height=8 \\ area=\frac{1}{2}(13+3)\times8 \\ area=\frac{26}{2}\times8 \\ area=13\times8 \\ area=104yd^2 \end{gathered}[/tex]For figure B
The figure is a parallelogram
The area of a parllelogram is given by
[tex]base\times height=13\times(15-8)=13\times7=91yd^2[/tex]Therefore, the total area is the sum of the areas of the two figures which will be
[tex]104+91=195yd^2[/tex]Thus, the area is 195 yd²
( 5/13 Marie made a $4,500 down payment on a car. The total cost of the car was $19,000. She made 50 equal monthly payments to pay the car in full. How much did Marie pay per month? Equation: Solution:
Answers
The total cost is $19,000, but Marie already did a payment of $4,500, so the remaining cost is:
[tex]19000-4500=14500[/tex]Now, this remaining cost was paid in 50 equal monthly payments, so in order to find the value of this monthly payment, we just need to divide the remaining cost by 50:
[tex]\frac{14500}{50}=\frac{1450}{5}=290[/tex]So Marie paid $290 per month.
Use the table of values for f and g below to find the indicated compositions.f(g(8))=Answerg(f(5))=Answerf(f(4))=Answerg(g(2))=Answer
Answers
Starting from the first question, we want:
[tex]f(g(8))[/tex]Let's start from the inside part:
[tex]g(8)[/tex]Since the inside of "g" is 8, this means we need to check for the row with x = 8, thay is, "8" in the column "x". Finding this row, we check the value in this row and column "g", which is "4".
This means that:
[tex]g(8)=4[/tex]Now, we can substitute this back in:
[tex]f(g(8))=f(4)[/tex]And we can do similarly. We check the row which has "4" in the "x" column and see the corresponding value in column "f". We can see that it is also "4", so, the answer for the first is:
[tex]f(g(8))=f(4)=4[/tex]Lastly, for the second, we do the same thing, the inside part is:
[tex]f(5)[/tex]So, we got to line x = 5 and check column "f". It is 0, so:
[tex]\begin{gathered} f(5)=0 \\ g(f(5))=g(0)_{} \end{gathered}[/tex]Now, we check row x = 0 and column "g" to find "9", so:
[tex]g(0)=9[/tex]Thus, the answer for the second is:
[tex]g(f(5))=g(0)=9[/tex]The 32 students in Mrs. Colby's class will share 80 slices of pizza equally. How many slices will each student get? Enter the correct answer to complete the statement. The students will each get slices. Explain how to get the fraction after you find the remainder. The slices leftover can each be cut in ? giving everyone another? v of a slice.
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The 32 students in Mrs. Colby's class will share 80 slices of pizza equally. How many slices will each student get? Enter the correct answer to complete the statement. The students will each get slices. Explain how to get the fraction after you find the remainder. The slices leftover can each be cut in ? giving everyone another? v of a slice.
step 1
Divide 80 by 32
80/32=40/16=20/8=10/4=5/2=2.5=2 1/2
each student get 2 1/2 slices
2 1/2=2+0.5=2+1/2
the fraction is 5/2
so
5/2=4/2+1/2=2+1/2=2 1/2
we have 32 students by 2 1/2
so
32 students by 2
32*2=64 slices
the remainder is
80-64=16 slices
divide 16 by 32
16/32=1/2
therefore
2+1/2=2 1/2
the answers part 2 are
The 16 slices leftover can each be cut in 2 half........giving everyone another (1/2) of a slice
create a linear equation in the slope-intercept form that contains points (2,8) and (6,-4)
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the two points are,
A(2,8)
B (6,-4)
the equation of the line in the slope intercept form is,
[tex]y-8=\frac{-4-8}{6-2}(x-2)[/tex][tex]\begin{gathered} y-8=\frac{-12}{4}(x-2) \\ y-8=-3x+6 \\ y=-3x+14 \end{gathered}[/tex]thus, the equation of the line is
y = -3x + 14
cambio siete decimos a una fracción igual Común denominador de 100
Answers
Answer:
70/100
Explicación:
2 fracciones son iguales si una de ellas puede ser calculada multiplicando el numerador y el denominador de la otra por el mismo número.
Por lo tanto, 7/10 es equivalente a:
[tex]\frac{7}{10}=\frac{7\cdot10}{10\cdot10}=\frac{70}{100}[/tex]Multiplicamos por 10 arriba y abajo para que el denominador fuera 100. De este modo obtemos que 7/10 es igual a 70/100.
Solve the equation by factoring. Separate multiple answers with a comma.
Answers
x = -4, 0, 6
Explanations:The given equation is:
[tex]x^3-24x=2x^2[/tex]The equation can be re-written as:
[tex]x^3-2x^2\text{ - 24x = 0}[/tex][tex]\begin{gathered} x(x^2\text{ - 2x - 24) = 0} \\ x\lbrack x^2\text{ - 6x + 4x - 24\rbrack = 0} \\ x\lbrack x(x-6)\text{ + 4(x - 6)\rbrack = 0} \\ x\text{ (x - 6) (x + 4) = 0} \\ x\text{ = 0} \\ x\text{ - 6 = 0} \\ x\text{ = 6} \\ x\text{ + 4 = 0} \\ x\text{ = -4} \end{gathered}[/tex]x = -4, 0, 6
A Factor with the distributive property Apply the distributive property to factor out the greatest common factor, 56+32 Stuck? Watch a video or use a hint.
Answers
the greatest commmon factor of 56 and 32 is 8
so in order to use the distributive property
8(7+4)=56+32=88
Describe the transformations: F(x) = - 3(x +1)^2 + 5 What is the Parent Function: Opens UP or DOWN:Stretch or Shrink: Vertical Movement Up or Down, how many units:Horizontal Movement Left or Right, how many units:
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You have the following transformation:
[tex]F(x)=-3(x+1)^2+5[/tex]The previous function if a parabola. the Parent Function of any parabola is:
[tex]y=x^2[/tex]All others parabolas can be obtained by applying transformation to the Parent Function.
If you expand the parenthesis of F(x), you obtain:
[tex]\begin{gathered} F(x)=-3(x^2+2x+1)+5=-3x^2-6x-3+5 \\ F(x)=-3x^2-6x+2 \end{gathered}[/tex]The dominant term, that is, the term with the variable x powered to 2, has a negative coefficient, it demands that the parabola open DOWN.
The coefficient of the dominant term is -3, then I-3I = 3 > 1. It means that the function stretches away from the x-axis.
The function streches way from x-axis by a factor of 3 units.
Vertical movement Up with 5 units. This is becasue the constant of the function, 5, which means the vertical translation of the Pater Function, if the constant is positive the translation is upward, if the translation is negative, it is downward.
Horizontal translation Left with 1 untit. The horizontal trasnlation is given by the constant term inside the quadratic parenthesis, in this case is + 1, whichi represents a translation of the graph to the left.
5. How much must be deposited now at 5% compounded semi-annually to yield an annuity payment of ₱30,000 at the beginning of each 6-month period for 6 years?
Answers
SOLUTION
Given the question in the question tab, the following are the solution steps to calculate the amount to be deposited
STEP 1: Write the formula for Future value annuity
[tex]FV=P\times\frac{(1+r)^n-1}{r}[/tex]Where:
FV = present value of an ordinary annuity
P=value of each payment
r=interest rate per period
n=number of periods
STEP 2: Write the given parameters
[tex]\begin{gathered} FV=30000,r=5,n=12,r=\frac{5}{100}=0.05,P=? \\ n=12\text{ because }6\text{months period for 6 years will be 2}\times6=12 \end{gathered}[/tex]STEP 3: Calculate the P
[tex]\begin{gathered} FV=P\times\frac{(1+r)^n-1}{r} \\ 30000=P\times\frac{(1+0.05)^{12}-1}{0.05} \\ 30000=P\times\frac{(1.05)^{12}-1}{0.05} \\ 30000=P\times\frac{(1.05)^{12}-1}{0.05} \\ 30000=P\times\frac{1.795856326^{}-1}{0.05} \\ 30000=P\times\frac{0.795856326^{}}{0.05} \\ 30000=\frac{0.795856326P^{}}{0.05} \\ By\text{ cross multiplication,} \\ 30000\times0.05=0.795856326P \\ 1500=0.795856326P \\ \frac{0.795856326P}{0.795856326}=\frac{1500}{0.795856326} \\ P=1884.762301 \\ P\approx1884.76 \end{gathered}[/tex]Hence, the amount that must be deposited now is approximately 1884.76 to the nearest cents
In an electrical circuit with resistors placed in parallel, thereciprocal of the total resistance is equal to the sum of thereciprocals of each resistance:
Answers
Answer:
C
[tex]R_2=16.16\Omega[/tex]Explanation:
Given the below equation;
[tex]\frac{1}{R_c}=\frac{1}{R_1}+\frac{1}{R_2}[/tex]We're also given;
[tex]\begin{gathered} R_1=25\Omega \\ R_c=10\Omega \end{gathered}[/tex]Let's substitute the given values into the equation, we'll have;
[tex]\frac{1}{10}=\frac{1}{25}+\frac{1}{R_2}[/tex]Let's subtract 1/25 from both sides of the equation;
[tex]\begin{gathered} \frac{1}{10}-\frac{1}{25}=\frac{1}{R_2} \\ \frac{5-2}{50}=\frac{1}{R_2} \\ \frac{3}{50}=\frac{1}{R_2} \end{gathered}[/tex]Let's cross multiply;
[tex]\begin{gathered} 3R_2=50 \\ R_2=\frac{50}{3} \\ R_2=16.16\Omega \end{gathered}[/tex]Show that when -9p2 + 4p + 1970 = 0, Total Revenue is at its maximum.Find the price and quantity which maximise Total Revenue.
Answers
Step 1
Write the demand function equation
[tex]Q=-9p^2+4p\text{ + 1970}[/tex]Step 2:
To find the price and quantity which maximize the revenue
You will find the derivative of Q with respect to price
[tex]\begin{gathered} \frac{dQ}{dp}\text{ = -18p + 4} \\ -18p\text{ + 4 = 0} \\ 18p\text{ = 4} \\ p\text{ = }\frac{4}{18}\text{ = }\frac{2}{9} \end{gathered}[/tex]Step 3:
Find the quantity demand by substituting p = 2/9
[tex]\begin{gathered} Q\text{ = -9 }\times\text{ (}\frac{2}{9})^2\text{ + 4 }\times\text{ }\frac{2}{9}\text{ + 1970} \\ =\text{ -0.44 + 0.888 + 1970} \\ =\text{ 1970.444} \\ =\text{ 1970} \end{gathered}[/tex]Final answer
The price which maximizes the total revenue is p = 2/9
The quantity is Q = 1970
11. A cylinder and a sphere both have the same radius, 4. The height of the cylinder isequal to the diameter of the sphere. Select the expression that describes thevolume of the cylinder that is not occupied by the sphere. (Use 3.14)A. 39.67B. 85.33T1 - 128TTC. 124.560D. 128TT – 85.33TT
Answers
Given that :
the radius of the cylinder and sphere = 4 units
the height of the cylinder (h) is equal to the diameter (d) of the sphere
the diameter of the sphere = 2 x radius = 2 x 4 = 8 units
also, the height of the cylinder = 8 units
The volume of the cylinder can be calculated using the formula:
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi\times4^2\times8 \\ V=128\pi \end{gathered}[/tex]The volume of the Cylinder
[tex]\begin{gathered} V=128\times3.14 \\ V=401.92uits^3 \end{gathered}[/tex]Answer:
Given that :
the radius of the cylinder and sphere = 4 units
the height of the cylinder (h) is equal to the diameter (d) of the sphere
the diameter of the sphere = 2 x radius = 2 x 4 = 8 units
also, the height of the cylinder = 8 units
The volume of the cylinder can be calculated using the formula:
The volume of the Cylinder
Step-by-step explanation:
Kaira's gross pay is $6,820. Her deductions total $917.27. What percent of her grosspay is take-home pay?Round to the nearest whole percent.
Answers
Answer:
87%
Explanation:
• Kaira's gross pay = $6,820
,• Deductions = $917.27
First, determine her take-home pay.
[tex]\begin{gathered} \text{Take}-\text{home Pay}=\text{Gross Pay-Deductions} \\ =6,820-917.27 \\ =\$5902.73 \end{gathered}[/tex]Next, determine what percent of her gross pay is her take-home pay.
[tex]\begin{gathered} \text{Percent}=\frac{\text{Take}-\text{Home Pay}}{\text{Gross Pay}}\times100 \\ =\frac{5902.73}{6820}\times100 \\ =86.55\% \\ \approx87\% \end{gathered}[/tex]87% of her gross pay is her take-home pay.
what the closest volume of a cylinder with a height of 10 and a circumference of 8
Answers
In order to calculate the volume of a cylinder, we can use the following formula:
[tex]V=\pi r^2h[/tex]Where r is the base radius and h is the height.
If the circumference is 8, we have:
[tex]\begin{gathered} C=2\pi r \\ 8=2\pi r \\ r=\frac{4}{\pi} \end{gathered}[/tex]Now, calculating the volume, we have:
[tex]\begin{gathered} V=\pi(\frac{4}{\pi})^2\cdot10 \\ V=\frac{160}{\pi} \\ V=50.93 \end{gathered}[/tex]So the correct option is the second one.
Only need help with finding the mean and standard deviation.
Answers
Given
Probability distribution table
Find
Mean and standard deviation
Explanation
mean for probability distribution is given by
[tex]mean=\sum_^xP(x)[/tex]so , mean
[tex]\begin{gathered} 0+0.25+0.54+0.36+0.64 \\ 1.79 \end{gathered}[/tex]standaed deviation
[tex]\begin{gathered} \sum_^x^2P(x) \\ 0+0.25+1.08+1.08+2.56 \\ 4.97 \end{gathered}[/tex]Final Answer
mean = 1.79
standard deviation = 4.97