We should know that :
1 pound = 16 ounces
The question is :
Which is more, 1/2 of a pound or 6 ounces?
so,
1/2 of a pound = 1/2 x 16 = 8 ounces
So,
8 ounces > 6 ounces
so, the answer is option 1
The more is 1/2 of a pound
A rock has a mass of 14 g and a volume of 2 cm3. What is the density of the rock? *
We will determine the density of the rock as follows:
[tex]\rho=\frac{14g}{2cm^3}\Rightarrow\rho=7g/cm^3[/tex]So, the density of the rock is 7 g/cm^3.
Construct a polar equation for the conic section with the focus at the origin and the following eccentricity and directrix.Conic Eccentricity Directrix1ellipsex= -75e =
In order to find the polar equation of the ellipse, first let's find the rectangular equation.
Since the directrix is a vertical line, the ellipse is horizontal, and the model equation is:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]Where the center is located at (h, k), the directrix is x = -a/e and the eccentricity is e = c/a.
So, if the eccentricity is e = 1/5 and the directrix is x = -7, we have:
[tex]\begin{gathered} \frac{c}{a}=\frac{1}{5}\rightarrow a=5c\\ \\ -\frac{a}{e}=-7\\ \\ \frac{a}{\frac{c}{a}}=7\\ \\ \frac{a^2}{c}=7\\ \\ \frac{25c^2}{c}=7\\ \\ 25c=7\\ \\ c=\frac{7}{25}\\ \\ a=5\cdot\frac{7}{25}=\frac{7}{5} \end{gathered}[/tex]Now, let's calculate the value of b with the formula below:
[tex]\begin{gathered} c^2=a^2-b^2\\ \\ \frac{49}{625}=\frac{49}{25}-b^2\\ \\ b^2=\frac{25\cdot49}{625}-\frac{49}{625}\\ \\ b^2=\frac{24\cdot49}{625}\\ \\ b^2=\frac{1176}{625} \end{gathered}[/tex]Assuming h = 0 and k = 0, the rectangular equation is:
[tex]\frac{x^2}{\frac{49}{25}}+\frac{y^2}{\frac{1176}{625}}=1[/tex]Now, to convert to polar form, we can do the following steps:
[tex]\begin{gathered} \frac{25x^2}{49}+\frac{625y^2}{1176}=1\\ \\ 600x^2+625y^2=1176\\ \\ 600(r\cos\theta)^2+625(r\sin\theta)^2=1176\\ \\ 600r^2\cos^2\theta+625r^2\sin^2\theta=1176\\ \\ r^2(600\cos^2\theta+625\sin^2\theta)=1176\\ \\ r^2=\frac{1176}{600\cos^2\theta+625\sin^2\theta}\\ \\ r=\sqrt{\frac{1176}{600\cos^2\theta+625\sin^2\theta}}\\ \\ r=\sqrt{\frac{1176}{600+25\sin^2\theta}} \end{gathered}[/tex]Another way of writing this equation in polar form is:
[tex]r=\frac{ep}{1+\sin^2\theta}[/tex]Where p is the distance between the focus and the directrix.
Since the foci are located at (±c, 0) = (±7/25, 0) and the directrix is x = -7, the distance is:
[tex]p=7-\frac{7}{25}=\frac{175}{25}-\frac{7}{25}=\frac{168}{25}[/tex]So the equation is:
[tex]\begin{gathered} r=\frac{\frac{1}{5}\cdot\frac{168}{25}}{1+\sin^2\theta}\\ \\ r=\frac{\frac{168}{125}}{1+\sin^2\theta}\\ \\ r=\frac{1.344}{1+\sin^2\theta} \end{gathered}[/tex]If A is the image of A(3, 4) after a dilation with scale factor 7 about the origin, what is the distance between A and A? Hint: Use the distance formula: d = √√(x₂ − x₂)² + (Y₂ − 3₂)² .
0 7 units
○28 units
O 30 units
O 35 units
Answer:
Step-by-step explanation:
you can view this,its similar just the numbers are switched.
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Answer:
35
Step-by-step explanation:
sorry if im wrong sorry
Jocelyn graphs a linear function that passes through three distinct points: A, B, and C. The coordinates ofpoint A (-3, -3) and point C (3,5) are shown.What are the possible coordinates of point B for Jocelyn’s linear function?
(0,1) is a possible coordinite through the points (-3,-3), (3,5)
Rick's average score on his first three tests in math is 80. What must he score on his next test to raise his average to 84?
SOLUTION
Now, we don't know the scores for his first three tests. But we are told that the average score for the first three tests was 80.
So, let the scores of the first three tests be a, b, and c. That means
[tex]\frac{a+b+c}{3}=80[/tex]Also, let's assume the total score for his first three tests was x, This means that
[tex]\begin{gathered} a+b+c=x \\ or \\ x=a+b+c \end{gathered}[/tex]Comparing with the first equation it means that
[tex]\begin{gathered} \frac{a+b+c}{3}=80 \\ \frac{x}{3}=80 \\ x=3\times80 \\ x=240 \end{gathered}[/tex]Now we are asked "What must he score on his next test to raise his average to 84?"
So this means the total tests becomes 4. Hence
[tex]\begin{gathered} \frac{a+b+c+d}{4}=84 \\ \frac{x+d}{4}=84 \\ \frac{240+d}{4}=84 \\ 240+d=84\times4 \\ 240+d=336 \\ d=336-240 \\ d=96 \end{gathered}[/tex]So he must score 96 to raise his average score to 84.
Hence, the answer is 96
What is the probability that a randomly selected oar was purchased in the 2010s given that the oar was made from ash wood?Simplify any fractions
P (A) = probability of a car purchased in 2010's
P (B) = probability of the car being made from ash wood
P (A and B) = 4
P (B) = 4 +3 = 7
Conditional probability:
P (B/A) = P (A and B ) / P (B) = 4 / 7 = 0.5714
You are clinic manager. You must schedule the equivalent of 1 1/2 nurses for each doctor on a shift, The friday day shift has 6 doctors scheduled How many nurses you will you need to schedule?
Data Given:
Nurses = 1 1/2 of each doctor
This can be interpreted as
[tex]\begin{gathered} 1\frac{1}{2}\text{ = }\frac{3}{2} \\ \\ 1\text{ Doctor requires }\frac{3}{2}\text{ times nurses} \end{gathered}[/tex]If there are 6 doctors in the day shift, then there will be
[tex]\frac{3}{2}\text{ x 6 nurs}es[/tex]=>
[tex]\begin{gathered} \frac{3\text{ x 6}}{2} \\ \\ =\text{ 3 x 3 } \\ \\ =\text{ 9 nurses} \end{gathered}[/tex]This means that I will have to schedule 9 nurses for the day shift on Friday
given AD is congruent to AC and AB is congruent to AE, which could be used to prove?
Answer
Option B is correct.
SAS | 2 sides and the angle between them in one triangle are congruent to the 2 sides and the angle between them in the other triangle, then the triangles are congruent.
Explanation
We have been told that the two triangles have two sets of sides that are congruent to each other.
And we can see that the angle between those congruent sides for the two triangles is exactly the same for the two triangles.
So, it is easy to see that thes two triangles have 2 sides that are congruent and the angle between these two respective sides are also congruent.
Hope this Helps!!!
A parabola opening up or
equation in vertex form.
down has vertex (-1, 4) and passes through (-2, 17). Write its equation in vertex form.
Equation of parabola in vertex form is 13x² + 26x + 17
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.
Given,
vertex (h,k) = (-1, 4)
points (x,y) = (-2, 17)
We know, The equation in vertex form is
y = a(x - h)² + k
put the (h,k) values,
y = a(x - (-1))² + 4
y = a(x + 1)² + 4 --------- eq(i)
Next, find the value of 'a' by plug in the points of (x, y) in eq(i)
y = a(x + 1)² + 4
⇒17 = a(-2 + 1)² + 4
⇒17 = a(-1)² + 4
⇒17 = a + 4
⇒a = 13
Now, substitute 'a' value in eq(i) to find the equation of parabola
y = a(x + 1)² + 4
⇒ y = 13(x + 1)² + 4
⇒ y = 13(x² + 1 + 2x) + 4
⇒ y = 13x² + 13 + 26x + 4
⇒ y = 13x² + 26x + 17
Therefore, equation of parabola in vertex form is 13x² + 26x + 17
To read more about the Parabola
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What is the midpoint of the line segment graphed below?10(5,9)(2-1)-1010- 10O A. (7,8)OB.OC (34)OD (710
ANSWER:
[tex](\frac{7}{2},4)[/tex]STEP-BY-STEP EXPLANATION:
To calculate the value of the midpoint, we use the formula of the midpoint which is the following:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Replacing and solving the midpoint:
[tex]\begin{gathered} (x_m,y_m)=(\frac{5+2_{}}{2},\frac{9-1_{}}{2}) \\ (x_m,y_m)=(\frac{7_{}}{2},\frac{8_{}}{2})=(\frac{7}{2},4) \end{gathered}[/tex]What are inequality? When do we use inequalities?What type of inequalities are there? Which symbols are used for each type?Are the following expressions variable inequalities? Why?a. 13z=27b. x<0c 3x+5x>11d. y+5≤11e. 7-1>- 32
Inequalities are expressions that refer to non-equivalent quantities. Inequalities can express less than, more than, less than or equal to, more than or equal to.
The type of inequalities and symbols are:
[tex]<,>,\leq,\ge[/tex]So, there are four types of inequalities, for example:
[tex]\begin{gathered} x<2 \\ x>2 \\ x\leq2 \\ x\ge2 \end{gathered}[/tex]Each inequality is different from the other, this means that the symbol used represents a type of inequality.
At last, among the choices, the inequalities are
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \\ 7-1>-32 \end{gathered}[/tex]However, variable inequalities mean that the inequalities must have a variable in it. So, they are:
[tex]\begin{gathered} x<0 \\ 3x+5x>11 \\ y+5\leq11 \end{gathered}[/tex]Therefore, the variable inequalities are b, c, and d.
Find the percent increase in volume when 1 foot is added to each dimension of the prism. Round your answer to the nearest tenth of a percent.7 ft10 ft86 ft
Solution
Step 1
The volume of a triangular prism = Cross-sectional area x Length
Step 2
[tex]\begin{gathered} Cross\text{ sectional area = area of the triangle} \\ Base\text{ = 6ft} \\ Height\text{ = 7ft} \\ Cross\text{ sectional area = }\frac{1}{2}\times\text{ 7 }\times\text{ 6 = 21 ft}^2 \\ Volume\text{ = 21 }\times\text{ 10 = 210 ft}^3 \end{gathered}[/tex]Step 3:
When 1 foot is added to each dimension of the prism.
The new dimensions becomes Base = 7, Height = 8 and length = 11
[tex]\begin{gathered} \text{Cross-sectional area = }\frac{1}{2}\text{ }\times\text{ 7 }\times\text{ 8 = 28 ft}^2 \\ Length\text{ = 11 ft} \\ Volume\text{ = 28 }\times\text{ 11 = 308 ft}^3 \end{gathered}[/tex]Step 4
Find the percent increase in volume
[tex]\begin{gathered} \text{Percent increase in volume = }\frac{308\text{ - 210}}{210}\text{ }\times\text{ 100\%} \\ \text{= }\frac{98}{210}\text{ }\times100 \\ \text{= 46.7} \end{gathered}[/tex]Final answer
46.7
Kara's original financial plan required that she save $220 amonth for two years in order to have $5,280 for the downpayment on a car. However, after one year she has onlymanaged to save $2,300. How much will Kara have to save each month in the second year in order to reach her original goal of $5,280?
given data:
the amount needed to pay the downpayment of the car = $5280.
original financial plan = $220 per month.
The amount kara saved after 1 year = $2300.
the balance amount she needed to save
[tex]\begin{gathered} =5280-2300 \\ =2980 \end{gathered}[/tex]now, divide the balance amount by 12, because 1 year =12 months.
[tex]\begin{gathered} =\frac{2980}{12} \\ =248.3 \end{gathered}[/tex]Thus, kara needs to save 248 dollors each month in order to have 5280 dollors after a year.
Domain and range from the graph of a piecewise function
The domain of the given function is:
[tex]\text{Domain}=\lbrack-3,-2\rbrack\cup\lbrack-1,5)[/tex]Because the domain corresponds to the set of all possible inputs, x-axis.
The range of this function is:
[tex]\text{Range}=\lbrack-5,3\rbrack[/tex]Because the range corresponds to the set of all possible outputs, y-axis.
eln(x-3) = 9what are the steps to solve? I am so confused, what is ln even??
A bucket can hold 26 litres of water when it is 8/9 full. How many litres can it hold when it is full?
Answer:
[tex]29.25\text{ liters}[/tex]Explanation:
Here, we want to know the amount of water the bucket can hold when full
Let us have the volume as x liters
Mathematically:
[tex]\begin{gathered} \frac{8}{9}\times x\text{ = 26} \\ \\ 8x\text{ = 9 }\times\text{ 26} \\ x=\text{ }\frac{9\times26}{8} \\ \\ x\text{ = 29.25 liters} \end{gathered}[/tex]answer step by step please suppose AC is congruent with AD. what information would you need to conclude that ADB is congruent with ACE using ASA theorem?
Answer:
Angle ABD must be congruent to Angle AEC.
Explanation:
Angle: Triangles ADB and ACE share angle A in common.
Side: AD is congruent to AC.
For Triangles ADB and ACE to be congruent by the ASA Congruence Theorem, then the following must hold:
Angle: Angle ABD must be congruent to Angle AEC.
Find the quantities indicated in the picture (Type an integer or decimal rounded to the nearest TENTH as needed.)
Remember that 3, 4 and 5 is a Pythagorean triple, since:
[tex]3^2+4^2=5^2[/tex]Since one side of the given right triangle has a length of 3 and the hypotenuse has a length of 5, then, the remaining leg b must have a length of 4.
Therefore:
[tex]b=4[/tex]The angles A and B can be found using trigonometric identities.
Remember that the sine of an angle equals the quotient of the lengths of the side opposite to it and the hypotenuse of the right triangle.
The side opposite to A has a length of 3 and the length of the side opposite to B is 4. Then:
[tex]\begin{gathered} \sin (A)=\frac{3}{5} \\ \sin (B)=\frac{4}{5} \end{gathered}[/tex]Use the inverse sine function to find A and B:
[tex]\begin{gathered} \Rightarrow A=\sin ^{-1}(\frac{3}{5})=36.86989765\ldotsº \\ \Rightarrow B=\sin ^{-1}(\frac{4}{5})=53.13010235\ldotsº \end{gathered}[/tex]Then, to the nearest tenth:
[tex]\begin{gathered} A=36.9º \\ B=53.1º \end{gathered}[/tex]Therefore, the answers are:
[tex]undefined[/tex]Equation of the line that passes through points (8,7) and (0,0)
Equation of the line:
y = mx+b
where:
m= slope
b= y-intercept
First, we have to find the slope:
m = (y2-y1) / (x2-x1)
Since we have:
(x1,y1) = (8,7)
(x2,y2)= (0,0)
Replacing:
m = (0-7)/ (0-8) = -7/-8 = 7/8
Now, that we have the slope:
y = 7/8 x +b
We can place the point (8,7) in the equation and solve for b:
7 = 7/8 (8) +b
7=7 +b
7-7=b
b=0
Since the y-intercept=0
The final equation is:
y= 7/8x
find the value of expression if d = 10 and c= 5, 5d + c + 2
Find the volume of the cone.9 cmr= 6 cmV = [?] cm3
The radius of cone is r = 6 cm.
The height of cone is h = 9 cm.
The formula for the volume of cone is,
[tex]V=\frac{1}{3}\pi\cdot r^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cone.
[tex]\begin{gathered} V=\frac{1}{3}\pi\cdot(6)^2\cdot9 \\ =339.29 \\ \approx339.3 \end{gathered}[/tex]Thus, volume of cone is 339.3 cm^3.
3. You have a bad cough and have to attend your little sister's choir concert. You take cough drops that contain 100 mg of menthol in each drop. Every minute, the amount of menthol in your body is cut in half. Write a funetion that models the amount of menthol in your body over time. Use x for minutes and y for the amount of menthol, in mg, remaining in your body It is safe to take a new cough drop after the level of menthol in your body is less than 5 mg, How long will it be before you can take another cough drop?
We have the next information
100 mg of menthol
every minute the amount of menthol in your body is cut in half
we have the next variables
x= minutes
y= amount of menthol in mg remaining in your body
so the equation that can we model is
[tex]y=100(0.5)^x[/tex]then we have that It is safe to take a new cough drop after the level of menthol in your body is less than 5 mg
y= 5mg
[tex]5=100(0.5)^x[/tex]in order to know the time we need to solve the equation above
[tex]\begin{gathered} (0.5)^x=\frac{5}{100} \\ (0.5)^x=0.05 \end{gathered}[/tex]then we isolate the x
[tex]x=4.32[/tex]after 5 minutes you can take another cough drop
The Thompson family and the Kim family each used their sprinklers last summer. The Thompson family's sprinkler was used for 25 hours. The Kim family'ssprinkler was used for 35 hours. There was a combined total output of 1075 L of water. What was the water output rate for each sprinkler if the sum of the tworates was 35 L per hour?Thompson family's sprinkler:Kim family's sprinkler:
Let x be the rate of water output by the Thompson family and let y be the rate of water output by the Kim family.
We know that the Thompson family sprinkler was used for 25 hours, Kim's family sprinkler was used for 35 hours and that there was a combined total output of 1075 L of water; then we have the equation:
[tex]25x+35y=1075[/tex]We also know that the combined water output was 35 L per hour, then:
[tex]x+y=35[/tex]Hence we have the system of equations:
[tex]\begin{gathered} 25x+35y=1075 \\ x+y=35 \end{gathered}[/tex]To solve this system we solve the second equation for y:
[tex]\begin{gathered} x+y=35 \\ y=35-x \end{gathered}[/tex]And we plug this value in the first equation and solve for x:
[tex]\begin{gathered} 25x+35(35-x)=1075 \\ 25x+1225-35x=1075 \\ -10x=1075-1225 \\ -10x=-150 \\ x=\frac{-150}{-10} \\ x=15 \end{gathered}[/tex]Once we have the value of x we plug it in the expression of y:
[tex]\begin{gathered} y=35-15 \\ y=20 \end{gathered}[/tex]Therefore we have that:
[tex]\begin{gathered} x=15 \\ y=20 \end{gathered}[/tex]which means:
Thompson family's sprinkler: 15 L per hour
Kim family's sprinkler: 20 L per hour.
Professor Ivy’s students have a Mean grade of 69.5 and a Standard Deviation of 6.5.3. If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be? (round to the tenthsplace)4. What percentile does Johnny’s score put him in? (round to the nearest whole number)
Given:
Mean,ц = 69.5
Standard deviation, σ = 6.5
Let's solve for the following:
• 3. If Johnny has an 82 in the class, what would the z-score for Johnny’s grade be?
Apply the z-score formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where:
x = 82
ц = 69.5
σ = 6.5
Thus, we have:
[tex]\begin{gathered} z=\frac{82-69.5}{6.5} \\ \\ z=\frac{12.5}{6.5} \\ \\ x=1.9 \end{gathered}[/tex]Therefore, the z-score is 1.9
Question 4.
Here, we are to find P(Z<1.9).
Using the standard normal distribution table, we have:
NORMSDIST(1.9) = 0.9712
Now convert to percentage:
0.9712 x 100 = 97.12% = 97%
ANSWER:
3). 1.9
4.) 97%
Find the area of a regularpolygon with 5 sides that has aside length of 6 inches and anapothem of 9 inches. Area = ?
SOLUTION
Write out the formula
[tex]\text{area of regular polygon=}\frac{A\text{ }\times P}{2}[/tex]where A= apothem and P= perimeter of the regular polygon
[tex]\begin{gathered} A=9in \\ P=6(5)=30in \\ \text{perimeter of the regular polygon is sum of all the lenght} \\ \text{the number of sides }\times the\text{ lenght of a side } \end{gathered}[/tex]The area of the regular polygon is
[tex]\frac{9\times30}{2}=9\times15=135in^2[/tex]x equals 6 y equals 1 y = x + ?
The given information is
draw a right triangle with a leg that as a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to nearest tenth.
Question:
Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.
Solution:
A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:
In this case, the appropriate trigonometric identity is:
[tex]\sin (55^{\circ})\text{ = }\frac{y}{h}[/tex]where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:
[tex]\sin (55^{\circ})\text{ = }\frac{10}{h}[/tex]and solving for h, we get:
[tex]h\text{ = }\frac{10}{\sin (55^{\circ})}\text{ = 12.207}\approx12.21[/tex]then, the correct answer is:
[tex]h\text{ =}12.21[/tex]Triangle XYZ is rotated 90° counterclockwise about the origin.The result is Triangle X'Y'Z', as shown below.
A shortcut for a 90° counterclockwise rotation:
• If the point (h, k) is rotated 90° counterclockwise rotation, then the final point will be (-k, h).
Answer:
Therefore the coordinates would be:
• X,(-5, 3) → ,X',(-3, -5)
,• Y,(-1, 1) → ,Y',(-1, -1)
,• Z,(-8, -4) → ,Z',(4, -8)
Then, the rule is (x, y) → (-y, x).
Question 19 of 25 Which of these is a factor in this expression? 6z^4 - 4+9 (y² +9) O A. (y +9 O B. 624 - 4 OC. 9 (y +9 OD. -4+9 (y +9)
1) In this expression, we have already a factored form. So the factor in this expression is 9(y³+9) Because multiplying "distributing it" we'll have the whole expression
6z^4 -4+9(y³+9)
6z^4 -4 +9y³+81
2) 9(y³+9)
Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 5 liters of natural oil for every 4 liters of synthetic oil. In order to make 531 litersof Petrolyn oll, how many liters of synthetic oil are needed?
The ratio 4 : 5 means that in every 9 liters of oil, we will have 4L of synthetic oil and 5L of natural oil.
Divide the 531 by 9 to get how many times we have to amplify the ratio:
[tex]\frac{531}{9}=59[/tex]Multiply the ratio by 59:
[tex]4\colon5\rightarrow(4)(59)\colon(5)(59)\rightarrow236\colon295[/tex]Meaning that for the 531L of oil, 236L would be synthetic and 295L natural.
Answer: 236 Liters.