# Recent questions and answers in Math

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### Charlene earns $\$150$more per week than her roommate Kristi, who earns$\$200$ less than her other roommate Sacha. Together the three friends earn $\$2050$per week. How much does each girl earn per week ? ### At a primate reserve, the mean age of all the male primates is 15 years, and the mean age of all female primates is 19 years. Which of the following must be true about the mean age$m$of all the combined group of male and female primates of the primate reserve ? ### If$\overline{PQ} \cong \overline{AB}$and$\overline{AB} \cong \overline{CD}$, then$\overline{PQ} \cong \overline{CD}$. Which of the properties below does the lines signify ? ###$d$and$m$are the parallel tangent at$A$and$B$. The tangent at$C$makes an intercept$DE$between$d$and$m$. Hence$\angle{DFE}$= ________ ### A line intersects the$y$axis and$x$axis at the points$P$and$Q$respectively. If$(2,-5)$is the mid point of$PQ$, then the coordinates of$P$and$Q$are ### An object has mass$m=\frac{p+1}{3p+1}$and density$\rho = \frac{p^2-1}{9p^2+6p+1}$. Determine the volume$v$where$\rho = \frac{m}{v}$. Also state the restrictions on any variables. ### The vertex of the parabola in the$x-y$plane above is$(0,c)$. Which of the following is true about the parabola with the equation$y=a(x-b)^2+c ?$### In a Rhombus$PQRS$, if$PQ=PR$, then$\angle{PQR} =$### Evaluate :$\large\frac{10+2i}{(3+i)(3-i)}\qquad (i=\sqrt{-1})$### A school district is forming a committee to discuss plans for the construction of a new high school. Of those invited to join the committee,$14\%$are parents of the students,$48\%$are teachers from the current high school,$28\%$are school and district administrators and the remaining$8$individuals are students. How many more teachers were invited to join the committee than school and district administrators ? ### A circle with centre$'O'$lies on the point$(3, -6)$and has centre$(0,0)$. What can be its radius ? ### A tank can be filled by one tap in 4 hours and another tap in 6 hours. How long will it take to fill the tank if both taps are opened together ? ### What values of a would make the given quadrilateral a parallelogram in the figure given below ? ### A godown measures :$40\; ft \times 25 \;ft \times 15\;ft$. What can be the maximum number of wooden crates each measuring$1.5 \;ft \times 1.25 \;ft \times 0.5 \;ft$that can be stored in godown ? ### Simplify :$(5\sqrt{2})^2 - (6\sqrt{3})^2$### If the$xy$plane, the graph of$y=x^2-16$intersects the graph$y=2x$at the points$(0,0)$and$(x,y)$. What are the values of$x$and$y$? ### Which of the following ordered pairs$(x,y)$satisfies the system of inequalities below ? <br>$\qquad y \leq 2x+3$<br>$\qquad x+y>3$### The total area of a city in Michigan is$102.1$square miles of which$13.1$square miles is water. If the city had a population of$621,000$people in the year$2012,$which of the following is closest to the population density in people per square mile of land area, of the city at that time ? ### During performing the experiment to find out the Latent heat of fusion ice, in a laboratory, when ice began to melt, the temperature remains at$0^{\circ}C$the liquid water that is formed with latent heat of fusion is also at$0^{\circ}C$. Which of the following graph represents this latent heat of fusion ? ###$\large\frac{y^2-5y-24}{9y^2-10y+16}=$### Given:$f(x)=2x^2-3x+5$, determine$f(-3)$### The factors of$x^4+2x^2+9$are ? ### If the sides of a rectangular field are$80$and$18\; ft$respectively, what will be the length of its diagonal ? ### Jack found a watch which was worth$\$540$ had an offer for sale at $\$450$during Thanks giving. What percent discount is offered during the sale? ### Allen sells stationery items in his shop. Since the sales was going on in a very slow process, he decreased the prices of the products by$10\%$. There by the number of products sold increased by$30\%$. What is the increase in the total revenue ? ### The circumference of a circle is$60\;cm$. An arc subtends$90^{\circ}$at the centre. Find its length. ### If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the greater of the two angles is ### The$n^{th}$term of a sequence is$7(n+5)$. Which is the first term to be larger than$100 $? ### The$n^{th} $term of a sequence is$7(n+5)$. What is the$100^{th}$term ? ### The$n^{th}$term of a sequence is$7(n+5 )$. What are the first four terms ? ### Write the expression (x + 5)(x + 2) as a polynomial in standard form. ### In a toy company , it required 36 machines to produce a certain number of car toys in 54 days . How many machines would be required to produce the same number of car toys in 81 days ? ### The graph below represents number of families with different number of members in a locality. <br> Read the bar graph given carefully and answer the following question. ### The graph below represents number of families with different number of members in a locality. <br> Read the bar graph given carefully and answer the following question. ### In the circle given below$\angle{PQR}=100^{\circ}$, where$P, Q$and$R$are points on a circle with centre$O.$Then$\angle{OPR}=$### The centre 'O' of a circle of radius 5. If$PT$is the tangent to the circle, whose length is$12$. What is the length of$OP$? ### School of Troy decided to award prizes to the most punctual and the most obedient student. The sum of two prizes is$\$150$ and this product is $\$5600.$Which of the following can be the equation to represent the above condition ? ### Which of the following equation can be the perpendicular to the equation$4x+5y=8$### In the figure given below$DE || AC$and$DF||AE$. Then which of the following statement is correct ? ### If$i=\sqrt{-1}$, what is the value of$i^{24}+i^{32}$### If$\sin \theta - \cos \theta = \frac{1}{2},$then the value of$\large\frac{1}{\sin \theta + \cos \theta} = $### In the diagram below if$\dfrac{y}{x}=5$and$\dfrac{z}{x}=4$, then the value of$x$is ### The perimeter increase in the area of a triangle if its each side is doubled is ### If$x^2+2xy+y^2=36$and$y-x=6$what is the value of$x$? ### What can be the equation of the line whose slope is$\frac{1}{7}$and y intercept 6 ? ### What can be the equation for the graph given below ? ### If$m^2-4n^2=32$and$m+2n=8$, what is the value of$m-2n?$### If$a=0.999,$which of the following is less than$a$? ### For any positive integer$n,\;n!$mean the product of all, integer from$1 $to$n$. What is the value of$\large\frac{1}{5!} + \frac{1}{4!}$### A circle with centre$O(-3,-4)\$ has a radius of 13 units. Which of the following can be its equation

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